Question

The domain of the function $f\left(x\right)=max\{\sin x,\cos x\}$ is $(-\infty ,\infty )$ The range of $f\left(x\right)$ is

• A. $[-\frac{1}{\sqrt{2}},1]$
• B. $[-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}]$
• C. $[0,1]$
• D. $[-1,1]$

Answer 1

Answer: (A)

$[-\frac{1}{\sqrt{2}},1]$

Here,$f\left(x\right)=max\{\sin x,\cos x\}$
From graph,range of $f\left(x\right)\in [-\frac{1}{\sqrt{2}},1]$
Hence,$\left(a\right)$ is the correct answer.