Question

The function $y=f\left(x\right)$ is defined by $x=2t-|t|,y=t^2+t|t|,t\in R$ in the interval $x\in [-1,1]$ then

• A. $f\left(x\right)$ is continuous everywhere
• B. $f\left(x\right)$ is not continuous at $x=0$
• 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 A $f\left(x\right)$ is continuous everywhere

$x=2t-|t|andy=t^2+t|t|fort>0x=2t-t=ty=2t^{2}f\left(x\right)=2x^{2}fort<0x=3tandy=0f\left(x\right)=0$

Clearly f(x) is continuous and differentiable everywhere

Hence, the answer is A