Let $f(x)=x^2$ and $g(x)=2^x$, then the

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let $f(x)=x^2$ and $g(x)=2^x$, then the solution set of $fog(x) = gof (x)$ is

Options:

$R$

{0}

{0, 2}

none of these

Correct Answer:

{0, 2}

Explanation:

$fog(x)=f(g(x))=f(2^x)=(2^x)^2=2^{2x}$ 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.