Mathematics - Functions Question with Solution | TestHub

Given $f(x)=x^3+5x+1$ Now $f^{\prime }(x)=3x^2+5>0,\forall x\in R$ $\therefore \mathrm{f}(\mathrm{x})$ is strictly increasing function $\therefore$ It is one-one Clearly, $f(x)$ is a continuous function and also increasing on $R$, ${\mathrm{Lt}}_{x\to -\infty }f(x)=-\infty$ and ${\mathrm{Lt}}_{x\to \infty }f(x)=\infty$ $\therefore \mathrm{f}(\mathrm{x})$ takes every value between $-\infty$ and $\infty$. Thus, $f(x)$ is onto function.