Let $\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}$ defined by $\mathrm{f}(\mathrm{x})=5 \mathrm{x}^4+2$. Then
Let $\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}$ defined by $\mathrm{f}(\mathrm{x})=5 \mathrm{x}^4+2$. Then
$f$ is one-one but not onto
$\mathrm{f}$ is onto but not one-one
$f$ is both one-one and onto
$\mathrm{f}$ is neither one-one nor onto
Solution
We have a function
$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$
at $f(x)=5 x^4+2$
$\operatorname{Sin} \theta f(-2)=f(+2)$
$\Rightarrow$ function is not one-one
and $\mathrm{f}(\mathrm{x}) \geq 2$
$\Rightarrow$ function is not on to.
hence function is neither one-one nor onto.