Question

Let $f:R\to R$ be defined be $f\left(x\right)=x^4,$ then

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

Answer 1

The correct option is D $f$ is neither one-one nor onto

$f\left(1\right)=f(-1)=1,$ so $f$ is not one-one.
$f$ cannot take any negative values, so its range cannot be equal to $R$, so $f$ is not onto