Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let \(f:\mathbb{R}\rightarrow\mathbb{R}\) defined by \(f(x)=(2-x^2)^{\frac{1}{2}}\) then \(f\circ f=\)

Options:

\(x^2\)

\(x\)

\(2x^2\)

\(2x\)

Correct Answer:

\(x\)

Explanation:

\(f(x)=(2-x^2)^{\frac{1}{2}}\)

so $fof(x)=(2-((2-x^2)^{\frac{1}{2}})^2)^{\frac{1}{2}}$

$=(2-2+x^2)^{\frac{1}{2}}=(x^2)^{\frac{1}{2}}$

$=x$