Question

The function $y=f\left(x\right)$ is defined by $x=2t-\left|t\right|,y=t^2+\left|t\right|,tϵR$ , then

• A. $f\left(x\right)$ is discontinuous at some points
• B. $f\left(x\right)$ is differntiable every where
• C. $f\left(x\right)$ is continuous but not derivable at $x=0$
• D. $f\left(x\right)$ is constant function

Answer 1

The correct option is B $f\left(x\right)$ is differntiable every where

If $t\ge o$ then $x=t,y=2t^2$

$\therefore y=2x^2,\ge 0$ $(\because 1=x)$

and for $+\angle ox=3t,y=0$ and $x<0(\because x=30)$

The function is defined as

$f\left(x\right)=2x^2$ if $o\le x\le 1$

if $-1\le x<o$

It is clear from the graph of (x), t (x) is differentiable and continues for all $xϵ[-1,1]$

[Hense the option (b)] is correct.