If f(x)=1-x/1+x, then f(f( x))=

Correct Answer is : cos⁡x xcosx

Correct Answer is : cos⁡x xcosx

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MHTCET 17 Apr 2026 Shift 2 Paper

Question : 117 of 150

Marks: +1, -0

f(x)=\frac{1-x}{1+x}

f(f(\cos x))=

Solution:

Concept:

A function can be applied to its own output by substituting the inner result into

f(x)

again.

Explanation:

Given

f(x)=\frac{1-x}{1+x}

First, find

f(\cos x)

by replacing

x

with

\cos x

f(\cos x)=\frac{1-\cos x}{1+\cos x}

Now apply

f

again to this result:

f(f(\cos x))=\frac{1-\frac{1-\cos x}{1+\cos x}}{1+\frac{1-\cos x}{1+\cos x}}

Simplify the numerator and denominator:

Numerator:

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

Denominator:

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

Dividing gives:

f(f(\cos x))=\frac{\frac{2\cos x}{1+\cos x}}{\frac{2}{1+\cos x}}=\cos x

Answer:

Option A:

\cos x

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