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} $

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- Sep 11th 2009, 10:03 PMxxlvhHaving 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} $ - Sep 11th 2009, 10:59 PMDefunkt
- Sep 12th 2009, 08:18 AMxxlvh
I have never solved an inequality involving a logarithm

- Sep 13th 2009, 07:11 PMxxlvh
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