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NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Functions

NDA 2023 · Mathematics · Functions

A function is defined by f(x)=π+ ^2 x What is the range of the...

A function is defined by

f(x)=\pi+\sin ^2 x

What is the range of the function?

Options

A $[0,1]$
B $[\pi, \pi+1]$
C $[\pi-1, \pi+1]$
D $[\pi-1, \pi-1]$

Correct answer

B. $[\pi, \pi+1]$

Step-by-step solution

Given a function

\mathrm{f}(\mathrm{x})=\pi+\sin ^2 \mathrm{x}

Since,

0 \leq \sin ^2 \mathrm{x} \leq

\mathrm{I}

\Rightarrow \pi \leq \pi+1 \sin ^2 \mathrm{x} \leq 1+\pi

So Range

=[\pi, \pi+1]

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