Question

If $f\left(x\right)=x^2$ and $g\left(x\right)=2^x$, then the solution set of the equation $f\left(2^x\right)=g\left(x^2\right)$ is

• A. $[0,2]$
• B. $R$
• C. $\{0,2\}$
• D. $R-[0,2]$

Answer 1

The correct option is C $\{0,2\}$

$f\left(2^x\right)=(2^x{)}^2,g(x^2)=2^{x^2}$
Given $f\left(2^x\right)=g\left(x^2\right)$
$\Rightarrow 2^{2x}=2^{x^2}$
$\therefore 2x=x^2\Rightarrow x^2-2x=0\Rightarrow x=0,2$

Hence, the solution set is $\{0,2\}$