# Thread: Having trouble finding domains...

1. ## Having trouble finding domains...

Find the domain of the following two functions:
1. $f(x) = \sqrt{\log_{0.5}\frac{x+3}{x-1}}$

2. $h(t) = \sqrt{2^{-t} + 1} + \arcsin\frac{2t}{1+t^2}$

2. Originally Posted by xxlvh
Find the domain of the following two functions:
1. $f(x) = \sqrt{\log_{0.5}\frac{x+3}{x-1}}$

2. $h(t) = \sqrt{2^{-t} + 1} + \arcsin\frac{2t}{1+t^2}$
You should note that the argument inside the square root must be non-negative, that the argument of the logarithm must be non-negative and that the argument of $arcsin$ must be between -1 and 1.

Can you solve this now?

3. I have never solved an inequality involving a logarithm

4. Okay concerning $\frac{x+3}{x-1} > 0$ I reached a solution of x < -3 or x > 1, hopefully that is correct.

However, I must be making an error when solving the inequality with the logarithm and I can't quite figure out where...
$\log_{0.5}\frac{x+3}{x-1} > 0$

$\log_{0.5}x+3 - \log_{0.5}x-1 > 0$

$\log_{0.5}x+3 > \log_{0.5}x-1$

$0.5^{\log_{0.5}x+3} > 0.5^{\log_{0.5}x-1}$

$x + 3 > x - 1$

$x + 2 > x$ true for all values of x? I'm really lost on this one
{"found_math": true, "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": 12, "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}