Question

Let $f\left(x\right)=3-\left|\sin x\right|$, then $f\left(x\right)$ is-

• A. Every where continuous
• B. Every where discontinuous
• C. Continuous only at $x=0$
• D. Discontinuous only at $x=0$

Answer 1

Answer: (A)

Every where continuous

$\sin x\&\left|x\right|$ are continuous functions

$\Rightarrow \left|\sin x\right|$ is continuous $\left[gof\left(x\right)\right]$

$3-\left|\sin x\right|$ is continuous

at $x=0$

${lim}_{x\to 0^{-}}f\left(x\right)={lim}_{x\to 0^{-}}(3+\sin x)=3+0=3$

${lim}_{x\to 0^{+}}f\left(x\right)={lim}_{x\to 0^{+}}(3-\sin x)=3-0=0$