If $f: R →R$ is defined by $f(x) =

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f: R →R$ is defined by $f(x) = \sin x+x$, then $f(f(x))$ is:

Options:

$2\sin x + 2x$

$\sin^2x+x^2$

$\sin(\sin x + x) + \sin x+x$

$\sin^2x+2\sin x+x$

Correct Answer:

$\sin(\sin x + x) + \sin x+x$

Explanation:

$f(x) = \sin x+x$

$f(f(x)) =\sin(\sin x + x) + \sin x+x$ (replacing $x$ with $\sin x + x$)