Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Which of the following function(s) from f: A → A are invertible, where x ∈ [−1, 1] ?

Options:

$f(x)=\frac{x}{2}$

$g(x)=\sin(\frac{πx}{2})$

$h(x) = |x|$

$k(x) = x^2$

Correct Answer:

$g(x)=\sin(\frac{πx}{2})$

Explanation:

Clearly (c) and (d) are ruled out as these are many-one. Also $f(x)=\frac{x}{2}$ is one-one but not
onto. $g(x)=\sin(\frac{πx}{2})$ is both one-one and onto.