Question

Let $R$ be the set of real numbers. If $f:R\to R$ is a function defined by $f\left(x\right)=x^4$, then $f$ is

• A. a surjective but not an injective function
• B. a bijective function
• C. an injective function but not a surjective function
• D. Neither an injective nor a surjective function

Answer 1

The correct option is D Neither an injective nor a surjective function

Given : $f\left(x\right)=x^4$
It is an even degree polynomial.
So,$f\left(x\right)$ is many-one function.
Also range of $f\left(x\right)$ is $[0,\infty )$ which is subset of $R$(co-domain)
So,$f\left(x\right)$ is into function
$\therefore$ $f$ is neither an injective nor a surjective function.