Question

If $f\left(x\right)$ and $g\left(x\right)$ are non-periodic functions, then $h\left(x\right)=f\left(g\right(x\left)\right)$ is

• A. non-periodic
• B. periodic
• C. may be periodic
• D. always periodic, if domain of $h\left(x\right)$ is a proper subset of real numbers.

Answer 1

The correct option is A non-periodic

Let $g\left(x\right)=2x$ & $h\left(x\right)={2x}^2.$

$h\left(g\right(h\left)\right)=2{\left(2x\right)}^2={8x}^2,$ which is also non-periodic.

Hence we can say that if $two$ functions are non-periodic, their composition will also be non-periodic.