Thank you for reporting, we will resolve it shortly
Q.
Let $f: R \rightarrow R$ be defined as $f(x)=x^4$.
Choose the correct option.
Relations and Functions - Part 2
Solution:
Function $f: R \rightarrow R$ is defined as $f(x)=x^4$
Let $x, y \in R$ such that $f(x)=f(y)$
$ \Rightarrow x^4 =y^4 $
$ \Rightarrow x=\pm y $ (considering only real values)
Therefore, $f\left(x_1\right)=f\left(x_2\right)$ does not imply that $x_1=x_2$
For instance, $f(1)=f(-1)=1$
Therefore, $f$ is not one-one.
Consider an element $-2$ in codomain $R$. It is clear that there does not exist any $x$ in domain $R$ such that $f(x)=-2$.
Therefore, $f$ is not onto. Hence, function $f$ is neither one-one nor onto.