Question

For real $x,$ let $f\left(x\right)=x^3+5x+1,$ then $\left(2009\right)$

• A. $f$ is one-one but not onto $R$
• B. $f$ is onto $R$ but not one-one
• C. $f$ is one-one and onto $R$
• D. $f$ is neither one-one nor onto $R$

Answer 1

The correct option is A $f$ is one-one but not onto $R$

Now,

$\begin{array}{c}f\left(x\right)=x^3+5x+1\\ f^{\prime }\left(x\right)=3x^2+5\\ so,fisone-one\end{array}$

Hence,

Option $A$ is correct answer.