Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If f(x) = 3x – 5, then$ f^{ -1} (x)$ is :

Options:

if given by $\frac{1}{3 x-5}$

is given by $\frac{x+5}{3}$

does not exist because f is not one – one

does not exist because f is not onto.

Correct Answer:

is given by $\frac{x+5}{3}$

Explanation:

Let  y=f(x)=3x5

Clearly f(x) is one-one onto function so it is invertible.

y=3x
$\Rightarrow x = \frac{y+5}{3}$
$\Rightarrow f^{-1}(x) = \frac{x+5}{3}$

(2) is the correct answer.