Q199 / 270 · NDA 2023 (Phase 2) · Mathematics

A function is defined by $f(x)=\pi+\sin ^2 x$ What is the range of the function?

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

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 $=[\pi, \pi+1]$

Hence, the correct answer is option: 'B'.

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