Question

Let f : $R\to R$ be defined as $f\left(x\right)=x^4.$ Choose the correct answer.

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

Answer 1

The correct option is A $f$ is one-one onto

$f:R\to R$ is defined as $f\left(x\right)=x^4$

Let $x,y\in R$ such that $f\left(x\right)=f\left(y\right)$

$\Rightarrow x^4=y^4$

$\Rightarrow x=\pm y$

$f\left(x_1\right)=f\left(x_2\right)\ne x_1=x_2$

$f\left(-1\right)=f\left(1\right)=1$

F is not me -me

Consider an element 2 in codomain R

Then it is clear $A$ any $x\in R$

Such that $f\left(x\right)=2$

So f is not onto

So f is neither one-one nor onto.