Question

Let $A=[-1,1]=B$ then which of the following functions from $A$ to $B$ is bijective function?

• A. $f\left(x\right)=\frac{x}{2}$
• B. $g\left(x\right)=\left|x\right|$
• C. $h\left(x\right)=x^2$
• D. $k\left(x\right)=\sin \frac{\pi x}{2}$

Answer 1

The correct option is D $k\left(x\right)=\sin \frac{\pi x}{2}$

For $f\left(x\right),$ co-domain will be confined to$[\frac{-1}{2},\frac{1}{2}]$
$g\left(x\right)=\left|x\right|,$ co-domain is $[0,1]$
$h\left(x\right)=x^2,$ co-domain is $[0,1]$
$K\left(x\right)=\sin \frac{\pi x}{2},$ co-domain is $[-1,1]$ and it is also one one in the same domain.
Hence $K\left(x\right)$ is bijective function