The range of $f(x)=\frac{1}{1+\sqrt{x}}$

CUET Preparation Today

Start Free Mocks

Home Questions QQVNNPFBPG

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The range of $f(x)=\frac{1}{1+\sqrt{x}}$ is equal to

Options:

$(0, \frac{1}{2}]$

[0, 1]

(0, 1]

none of these

Correct Answer:

(0, 1]

Explanation:

$0≤\sqrt{x}<∞⇒1≤1+\sqrt{x}<∞⇒0<\frac{1}{1+\sqrt{x}}≤1⇒0<f(x)≤1$