Let $ƒ: R → R$ be a function defined as $f(x) = x^4$. Which one of the following is true?

$f$ is neither one-one nor onto.

The correct answer is Option (4) → $f$ is neither one-one nor onto.

Given function $f:R\rightarrow R$ defined by $f(x)=x^4$.

Check one–one:

$f(1)=1^4=1$ and $f(-1)=(-1)^4=1$

$f(1)=f(-1)$ but $1\neq -1$

So $f$ is not one–one.

Check onto:

For $y=-1\in R$, there is no real $x$ such that $x^4=-1$.

So $f$ is not onto.

$f$ is neither one–one nor onto.