Let $f(x)=x^2$ and $g(x)=2^x$, then the solution set of $fog(x) = gof (x)$ is
Answer & explanation
Correct answer: option 3
$fog(x)=f(g(x))=f(2^x)=(2^x)^2=2^{2x}$ and $gof(x)=g(f(x))=g(x^2)=2^{x^2}$
Thus the solution of $2^{2x}=2^{x^2}$ is given by $x^2= 2x$ which is x = 0, 2.