If $f(x)=\frac{1}{1-x}$, then for $x>

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $f(x)=\frac{1}{1-x}$, then for $x>1$, $f(x)$ is:

Options:

decreasing

constant

increasing

neither decreasing nor increasing

Correct Answer:

increasing

Explanation:

$f(x)=\frac{1}{1-x}=(1-x)^{-1}$

so, $f'(x) = (-1)×(1-x)^{-2}×\frac{d}{dx}(1-x)$

$=(-1)×(-1)×(1-x)^{-2}$

$=\frac{1}{(1-x)^2}>0$ always

$f(x)$ is increasing always