Question

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

• A. f may be one-one and onto
• B. f is 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

Given $f:R\to R$ defined by $f\left(x\right)=x^4$
Since $-2$ and $2$ are in the domain and $f(-2)=4=f\left(2\right)$
Thus, $-2$ and $2$ have same images under $f$

Hence, $f$ is not a one-one function.

Also, there is no real number which maps to $-2$ or any other negative real number in co-domain because if

$x^4=-2\Rightarrow x=\pm \sqrt{-2},$ which is not a real number

Hence, $f$ is not onto function
$\therefore f\left(x\right)$ is neither one-one nor onto.