If $f(x)=\frac{4x+5}{x-6}, x\neq 6$ th

CUET Preparation Today

Start Free Mocks

Home Questions GEWEX82GDP

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f(x)=\frac{4x+5}{x-6}, x\neq 6$ then $f^{-1}(x)$ is equal to

Options:

$\frac{5x+6}{x+4},x\neq -4$

$\frac{5x+6}{x-4},x\neq 4$

$\frac{6x+5}{x-4},x\neq 4$

$\frac{6x+5}{x+4},x\neq -4$

Correct Answer:

$\frac{6x+5}{x-4},x\neq 4$

Explanation:

$y=\frac{4x+5}{x-6}$

so $xy-6y=4x+5⇒x(y-4)=6y+5$

so $x=\frac{6y+5}{y-4},y≠4$

$f^{-1}(x)=\frac{6x+5}{x-4},x≠4$