Question

Function $f:R\to R,f\left(x\right)=x^3-x$ is

• A. one-one onto
• B. one-one into
• C. many-oine onto
• D. many-one into

Answer 1

The correct option is A one-one onto

$f\left(x\right)=x^3-x$

$f\left(x\right)=x(x^2-1)=x(x-1)(x+1)$

$0,1,-1$

$f^{\prime }\left(x\right)=3x^2-1$

$\Rightarrow 0$

$x=dfrac\pm 1\sqrt{3}$

$\Rightarrow$ One one onto function.