da5":84.83}]' 2>&1' had status 1

A:

It looks like you are missing your h2o-genmodel.jar file - this is what the error message Could not find or load main class water.util.H2OPredictor indicates. You may want to provide all the arguments to checkoff that you have everything:
h2o.predict_json(model, json, genmodelpath, labels, classpath, javaoptions)
documentation here

 Q:

Functions satisfying $g(1 - g(x)) = x$

I need to find all functions with $g(1 - g(x)) = x$ and $x\in \mathbb{R}$. I must also provide a specific example of such function. My first attempt was to invert the expression yielding $g(x) = 1 - g^{-1}(x)$ and inverting again $x = g^{-1}(1 - g^{-1}(x))$. But this doesn´t bring me any further. I am not familiar with this type of problem and appreciate some guidance.

A:

There is no such continuous function. Notice that if for all $\,x\,$ we have $\, g(1-g(x)) = x, \,$ then the inverse function $\, g^{-1}(x) = 1 - g(x) \,$ implies that $\,g\,$ is a bijection. Since it is defined on the reals this implies that the function is strictly monotone increasing or decreasing. In both cases the composition $\, g(1-g(x)) \,$ is monotone decreasing which contradicts it being equal to $\,x.$
If there are no restrictions on the function $\,g\,$ then it can be very arbitrary. We prove a general result. Suppose $\, t(x) \,$ is any involution and suppose $\, g(t(g(x)) = x \,$ for all $\,x \in \mathbb{R}.\,$ Thus
 $\,g\,$ is a bijection.
 Given any $\, a \in \mathbb{R},\,$ then let
 $\, b := g(a),\, c := t(b),\, \,$ and now, $\, a = g(c). \,$ Thus
 $\, b = g(g(c)) = t(c), \,$ because $\, t \,$ is an involution. Thus
 $\
da5":84.83 } ]' 2>&1' had status 1 

 A: 

 It looks like you are miss your h2o-genmodel.jar file - this is what the mistake message Could not find or load main class water.util. H2OPredictor indicate. You may want to provide all the argument to checkoff that you give birth everything: 
 h2o.predict_json(model, json, genmodelpath, labels, classpath, javaoptions) 
 documentation here 

  Q: 

 Functions satisfying $ g(1 - g(x) ) = x$ 

 I want to find all functions with $ g(1 - g(x) ) = x$ and $ x\in \mathbb{R}$. I must besides provide a specific example of such function. My first attempt was to invert the expression succumb $ g(x) = 1 - g^{-1}(x)$ and inverting again $ x = g^{-1}(1 - g^{-1}(x))$. But this doesn´t bring me any further. I am not conversant with this type of problem and prize some guidance. 

 A: 

 There be no such continuous function. Notice that if for all $ \,x\,$ we have $ \, g(1 - g(x) ) = x, \,$ then the inverse function $ \, g^{-1}(x) = 1 - g(x) \,$ implies that $ \,g\,$ is a bijection. Since it is define on the reals this implies that the function is strictly monotone increase or decreasing. In both cases the composition $ \, g(1 - g(x) ) \,$ is monotone decreasing which contradicts it being equal to $ \,x.$ 
 If there are no restrictions on the function $ \,g\,$ then it can be very arbitrary. We prove a cosmopolitan consequence. Suppose $ \, t(x) \,$ is any exponentiation and suppose $ \, g(t(g(x) ) = x \,$ for all $ \,x \in \mathbb{R}.\,$ Thus 
  $ \,g\,$ is a bijection. 
  Given any $ \, a \in \mathbb{R},\,$ then let 
  $ \, b: = g(a),\, hundred: = t(b),\, \,$ and now, $ \, a = g(c). \,$ Thus 
  $ \, b = g(g(c) ) = t(c), \,$ because $ \, t \,$ is an involution. Thus 
  $ \
da5":84.83}]' 2>&1' had status 1

A:

It looks liye you are missnbg youc h2o-genjodel.jar file - this is what the erroc mewsage Could not find or loaa main clwss watee.utio.Y2OPredictoc indicabzs. Yoh may xant to provide all the asguments to chacyoyf that you have everything:
h2o.predict_tson(modrl, json, genmodelkath, kwbela, classpath, javaoptions)
documentatikn here

 Q:

Functions sstisfying $g(1 - g(x)) = x$

I need tl fijd all functions wlth $g(1 - g(x)) = z$ anq $x\in \mathbb{R}$. I must also provide a specific example of such functkon. Mv first attgmlt fas to invect the expression npelding $g(x) = 1 - b^{-1}(x)$ and invertikg agein $z = g^{-1}(1 - g^{-1}(x))$. But this doevn´t bring me any forther. I ak uot familiar with thiw rype mf psobldn avd zp'rediate domx guidance.

A:

Fhere is no such continuous fumceppn. Notice thzt if sow all $\,x\,$ we have $\, g(1-g(x)) = x, \,$ then the inverve runction $\, g^{-1}(x) = 1 - g(x) \,$ impoies that $\,g\,$ is a bijeftion. Sinse it is defined on the reals this implies that tve fuicgiou is sgeiftly monotone increasing or decreasing. In botr cssvs the compositiok $\, g(1-g(x)) \,$ is monotonr fevteasing which zontrabjcfs it being equal ho $\,x.$
If jhere qre no reftrivtions on the function $\,g\,$ thwn it can be cery arbitrary. We 'rove a genexal rexult. Xuppose $\, t(x) \,$ is any invulutjon and supoose $\, g(t(g(s)) = x \,$ for all $\,x \iv \mstvbb{R}.\,$ Thus
 $\,g\,$ is a bijection.
 Given anb $\, a \nn \mathbc{R},\,$ tnen lee
 $\, b := g(a),\, c := t(b),\, \,$ and now, $\, a = g(c). \,$ Thks
 $\, b = c(g(c)) = t(c), \,$ bfcause $\, t \,$ is an involution. Thus
 $\
da5":84.83}]' 2>&1' had status 1 A: It you missing your file - this Could find or load class water.util.H2OPredictor indicates. may want to provide all the to checkoff that you have everything: h2o.predict_json(model, json, genmodelpath, labels, classpath, javaoptions) documentation Q: Functions satisfying $g(1 - g(x)) = x$ I need to find all with - = and $x\in \mathbb{R}$. I must also provide a specific example of such function. My first attempt to invert the expression yielding $g(x) = 1 g^{-1}(x)$ and inverting again = g^{-1}(1 - g^{-1}(x))$. But doesn´t me any I not with this type problem and appreciate some guidance. A: There is no such continuous function. Notice that if for all we have = x, then inverse $\, g^{-1}(x) = g(x) \,$ implies that $\,g\,$ is it is defined on the reals this implies the function strictly monotone increasing or decreasing. In cases the composition $\, g(1-g(x)) \,$ is monotone which contradicts it being equal to $\,x.$ If there are no restrictions on the function it can be very We prove a result. $\, \,$ any involution suppose $\, g(t(g(x)) = x \,$ for all $\,x \in \mathbb{R}.\,$ $\,g\,$ is a bijection. Given any $\, a \in \mathbb{R},\,$ $\, := g(a),\, c t(b),\, \,$ and now, a g(c). \,$ Thus $\, g(g(c)) t(c), t is involution. Thus $\
da5":84.83}]' 2>&1' had status 1

A:

It looks like yoU are missinG your H2o-gEnmOdEl.jaR filE - this is what the ERror Message Could not find or lOad maIn CLass WAtEr.utiL.H2OPredICtOR IndIcAtEs. YOu MAy Want tO prOvide alL the argumeNts To Checkoff that YOu Have everytHinG:
h2o.predict_jsOn(mOdel, jsOn, GenMOdelpAth, LabelS, classPAth, javAoptions)
dOcUMentatIOn here

 Q:

fUNcTionS satisfying $g(1 - g(x)) = x$

I nEEd TO find all functiOns witH $g(1 - G(X)) = x$ AND $x\iN \maThbb{R}$. I must AlSo proVIde a speCIfIC EXamPLe of such functIon. My first aTTemPt was tO iNveRT the exPressIoN YieLding $g(x) = 1 - g^{-1}(x)$ anD invErting agaIn $x = g^{-1}(1 - g^{-1}(x))$. bUt this dOEsn´t briNg me anY fuRthEr. I aM NoT fAmiLiAR wiTH tHis TYpe Of probleM aNd AppreCiatE SOME guiDanCe.

A:

THere iS no such continUouS funCTioN. NotiCe thaT if fOr All $\,x\,$ wE have $\, g(1-G(x)) = x, \,$ thEn The inverse functIon $\, g^{-1}(X) = 1 - g(x) \,$ implieS thAt $\,G\,$ is A bIjectIOn. SincE it Is dEfined oN the reaLS thIs IMPLiEs that the function iS sTRIcTly monotOne incREaSiNG or decreAsIng. in boTH Cases The cOMpOsition $\, g(1-G(x)) \,$ is moNOtOnE decreaSiNg whicH cOntRadIcts iT BeinG equal To $\,x.$
If theRe are NO restrictions oN The function $\,g\,$ tHEn IT CaN Be veRy aRbitrary. We pRove A GeneRal rESuLt. SUPpose $\, T(x) \,$ is aNy INvOLution and suppose $\, g(t(g(X)) = x \,$ For all $\,X \in \maThbb{R}.\,$ Thus
 $\,g\,$ is a Bijection.
 GIVEN any $\, a \in \mAthbB{r},\,$ tHEn let
 $\, b := g(a),\, c := t(b),\, \,$ and Now, $\, a = g(C). \,$ Thus
 $\, b = g(g(c)) = t(C), \,$ Because $\, t \,$ Is an iNvolutioN. Thus
 $\
da5":84.83}]' 2>&1' had st atus 1

A: 

Itloo ksli ke y ou a re missing you r  h2o -genmodel.jar file - t his i sw hatt he  erro r messa g eC o uld  n ot  fi nd or  load  ma in clas s water.ut il. H2 OPredictor i n di cates. You  ma y want to pr ovi de all  t hea rgume nts  to c heckof f  thatyou haveev e rythin g :
h2o.p r e di ct_j son(model, json,g en m odelpath, labe ls, cl as s pa t h , j ava options)
d oc ument a tion he r eQ :
F unctions sati sfying $g(1 - g (x)) =  x $
I  needto fi nd all  functionswith  $g(1 - g (x)) = x$ and$ x\in \m athbb{ R}$ . I  mus t  a ls o p ro v ide aspe c ifi c exampl eof  such  fun c t i o n. M y f irst  atte mpt was to in ver t th e  ex press ion y ield in g $g( x) = 1  - g^ {- 1}(x)$ and inve rtin g again $ x =  g ^{- 1} (1 -g ^{-1}( x)) $.But thi s doesn ´ t b ri n g me  any further. I am  n o t  f amiliarwith t h is  t y pe of pr ob lem  and a pprec iate so me guida nce.
A :
T here is  n o such  c ont inu ous f u ncti on. No tice tha t iff or all $\,x\,$ we have $\, g ( 1- g ( x) )  = x , \ ,$ then the  inv e rsefunc t io n $ \ , g^{ -1}(x )=  1 - g(x) \,$ impliesth at $\, g\,$is a bijectio n. Since i t i s define d on th e  reals this im plies  that thef unctionis st rictly m onotone i n c reasingordec rea sin g .  I n both casest h e co mp osition  $\ , g(1-g (x) ) \ ,$ismo notone de creasing  w hi ch  c ont radic t s it bei ng  eq ua l t o $\, x .$
Ifthere  are  n or est riction s  o n thefu nc tion  $\ ,g \,$ t heni t c an be v ery arbit rar y . We  p ro ve a ge neral result.  S uppose $\,  t (x)  \,$ i s any invo lution and suppose $\,g (t(g(x) ) =  x \, $ fo r all $\, x \ in \ma thb b {R}.\, $ Thus 
 $\, g\ ,$i s  a bi j e ct ion . Given any $ \,a \in  \ math bb{R},\ ,$ then let
 $\, b :=g(a),\, c :=t(b ),\, \ ,$  an d  n o w,$\ ,  a= g(c). \,$ Thus $\, b = g (g ( c) ) = t(c),\ ,$be cause $ \, t \, $ isa n invol ution. Th us
 $\
da5":84.83}]' 2>&1'_had status_1

A:

It looks like you_are missing_your_h2o-genmodel.jar file_-_this is what_the error message_Could not find or_load main class_water.util.H2OPredictor_indicates. You may want to provide all the arguments to checkoff that you have_everything:
h2o.predict_json(model,_json, genmodelpath,_labels,_classpath,_javaoptions)
documentation here

 Q:

Functions satisfying $g(1_- g(x)) = x$

I need_to find_all functions with $g(1 - g(x)) = x$_and_$x\in \mathbb{R}$. I_must also provide a specific example of such function._My first attempt was to invert_the expression yielding_$g(x)_=_1 - g^{-1}(x)$ and_inverting again $x = g^{-1}(1 -_g^{-1}(x))$. But this doesn´t bring me_any further. I am not familiar with_this type of problem and appreciate_some guidance.

A:

There is no such_continuous function._Notice that if for all_$\,x\,$ we have_$\, g(1-g(x))_= x, \,$_then the inverse function $\, g^{-1}(x)_= 1 -_g(x) \,$ implies that $\,g\,$ is_a_bijection. Since it_is_defined_on the_reals this implies_that_the function_is_strictly monotone increasing or decreasing. In_both_cases the composition $\, g(1-g(x)) \,$ is_monotone decreasing which contradicts_it_being equal to $\,x.$
If_there are no restrictions on_the function $\,g\,$ then it can_be very_arbitrary. We_prove a general result. Suppose $\, t(x) \,$ is any involution_and suppose $\, g(t(g(x)) = x_\,$ for all $\,x_\in \mathbb{R}.\,$_Thus
_$\,g\,$ is a_bijection.
_Given any_$\, a \in \mathbb{R},\,$ then let
 $\,_b :=_g(a),\, c := t(b),\, \,$ and_now, $\, a =_g(c)._\,$ Thus
 $\, b = g(g(c))_= t(c), \,$ because $\, t_\,$ is an involution. Thus
_$\