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} $
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