If $f:[1, \infty) \rightarrow[2, \infty)

CUET Preparation Today

Start Free Mocks

Home Questions 3QM3J9ABD5

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f:[1, \infty) \rightarrow[2, \infty)$ is given by $f(x)=x+\frac{1}{x}$ then $f-1(x)$ equals :

Options:

$\frac{x+\sqrt{x^2-4}}{2}$

$\frac{x}{1+x^2}$

$\frac{x-\sqrt{x^2-4}}{2}$

$1+\sqrt{x^2-4}$

Correct Answer:

$\frac{x+\sqrt{x^2-4}}{2}$

Explanation:

$y=x+\frac{1}{x}$ so $yx=x^2+1⇒x^2-yx+1=0$

so $x=\frac{y±\sqrt{y^2-4}}{2}$ $f^{-1}(x)=\frac{x±\sqrt{x^2-4}}{2}$

as $x∈(1,∞)$

so $f^{-1}(x)=\frac{x+\sqrt{x^2-4}}{2}$