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NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Functions

NDA 2024 · Mathematics · Functions

Paragraph: Let f ^ g(x)= ^2 x and g ^ f(x)=| x| . Question: Which...

Paragraph: Let

f {}^{\circ} g(x)=\cos ^2 \sqrt{x}

and

g {}^{\circ} f(x)=|\cos x|

.
Question: Which one of the following is

g(x)

?

Options

A $\sqrt{x}$
B $|x|$
C $x^2$
D $x|x|$

Correct answer

A. $\sqrt{x}$

Step-by-step solution

If

\mathrm{f}(\mathrm{x})=\cos ^2 \mathrm{x}

then

\mathrm{g}(\mathrm{x})=\sqrt{\mathrm{x}}

, so that fog

(x)=\cos ^2 \sqrt{x}

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