Question

Let $f$ : $R\to R$ be any function. Defined as $g:R\to R$ by $g\left(x\right)=|f\left(x\right)|,\forall x$. Then $g$ is

• A. onto if $f$ is onto
• B. one-one if $f$ is one-one
• C. continuous if $f$ is continuous
• D. diferentiable if $f$ is differentiable

Answer 1

The correct option is C continuous if $f$ is continuous

$g\left(x\right)=\left|f\left(x\right)\right|$

Let $h\left(f\left(x\right)\right)=g\left(x\right)$

Where $h\left(x\right)=\left|x\right|$

We know that $\left|x\right|$ is continuous everywhere

$\therefore$ if f is continuous

Then $h\left(f\left(x\right)\right)$ is continuous

$g\left(x\right)$ is continuous.