# Thread: Having trouble finding domains...

1. ## Having trouble finding domains...

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

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

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

2. $\displaystyle h(t) = \sqrt{2^{-t} + 1} + \arcsin\frac{2t}{1+t^2}$
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 $\displaystyle arcsin$ must be between -1 and 1.

Can you solve this now?

3. I have never solved an inequality involving a logarithm

4. Okay concerning $\displaystyle \frac{x+3}{x-1} > 0$ 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...
$\displaystyle \log_{0.5}\frac{x+3}{x-1} > 0$

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

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

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

$\displaystyle x + 3 > x - 1$

$\displaystyle x + 2 > x$ true for all values of x? I'm really lost on this one