Question

The range of the function $f\left(x\right)=\sin \left[\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right]$ is

• A. $[-1,1]$
• B. $(-1,1)$
• C. $[-1,1)$
• D. cannot be determined

Answer 1

The correct option is A $[-1,1]$

$f\left(x\right)=\sin \left[\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right]$
$f\left(x\right)$ will be defined if $\frac{\sqrt{4-x^2}}{1-x}>0$ & 4 - $x^2$ > 0
$\Rightarrow -2<x<1\&-\infty <\log \frac{\sqrt{4-x^2}}{1-x}<\infty$
$-1\le \sin \left[\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right]<1$
so range of $f\left(x\right)$ is $[-1,1]$