Having trouble finding domains...

**xxlvh** · Sep 11th 2009, 10:03 PM

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

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

**Defunkt** · Sep 11th 2009, 10:59 PM

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?

**xxlvh** · Sep 12th 2009, 08:18 AM

I have never solved an inequality involving a logarithm

**xxlvh** · Sep 13th 2009, 07:11 PM

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

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