Question

If $f:R\to R,f\left(x\right)=x^3+x$, then $f$ is

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

Answer 1

The correct option is A one-one onto

$f^{\prime }\left(x\right)=3x^2+1>0$ for all values of $x$
Therefore, $f$ is strictly increasing
Thus one-one
and range of $f$ is $(-\infty ,\infty )$
Therefore, f is onto