Question

Find the domain of definition of the following function.
$y={\left(\frac{1}{2}\right)}^{\sqrt{4-x^2}}+\frac{1}{x-1}.$

Answer 1

$y={\left(\frac{1}{2}\right)}^{\sqrt{4-x^2}}+\frac{1}{x-1}$

$4-x^2\ge 0$

$x-1\ne 0$

$-x^2\ge -4$

$x^2\le 4$

$-2<x<2$

$x-1\ne 0$

$x\ne 1$

So, the domain of $y$ is $[-2,2]-\left\{1\right\}$