Practicing Success

Target Exam

CUET

Subject

Mathematics

Chapter

Relations and Functions

Question:

f: R → R given by $f (x) = x + \sqrt{x^2}$, is

Options:

injective

surjective

bijective

none of these

Correct Answer:

none of these

Explanation:

The correct answer is Option (4) → none of these

We have,

$f(x) = x + \sqrt{x^2} = x+|x|=\left\{\begin{matrix}2x,&x≥0\\x-x=0,&x<0\end{matrix}\right.$

Clearly, f is many-one into function.