Inverse of a function

Chapter 1 Class 12 Relation and Functions
Serial order wise

### Transcript

Ex 1.3, 2 (Introduction) Let f, g and h be functions from R to R. Show that (f + g)oh = foh + goh (f.g)oh = (foh).(goh) Let f(x) = x, g(x) = sin x , h(x) = log x We will show (f + g) oh = foh + goh Let f(x) = x, g(x) = sin x , h(x) = log x To prove: We will show (f .g) oh = foh . goh (f .g) oh = foh . goh Ex 1.3, 2 Let f, g and h be functions from R to R. Show that (f + g)oh = foh + goh & (f.g) oh = (foh).(goh) Proving (f + g) oh = foh + goh L.H.S (f + g)oh = (f + g) (h(x)) = f (h(x)) + g (h(x)) = foh + goh = R.H.S Hence, (f + g) oh = foh + goh Proving (f .g) oh = foh . goh L.H.S (f . g)oh = (f . g) (h(x)) = f (h(x)) . g (h(x)) = foh . goh = R.H.S Hence, (f . g) oh = (foh) . (goh)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}