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# Solution for If G (X) is a Decreasing Function On R And F(X) = Tan−1 [G (X)]. State Whether F(X) is Increasing Or Decreasing On R ? - CBSE (Science) Class 12 - Mathematics

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ConceptIncreasing and Decreasing Functions

#### Question

If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing on R ?

#### Solution

$\text { Given }:g\left( x \right)\text { is decreasing on R }.$

$\Rightarrow x_1 < x_2$

$\Rightarrow g\left( x_1 \right) > g\left( x_2 \right)$

$\text {Applying tan}^{- 1} \text { on both sides, we get }$

$\Rightarrow \tan^{- 1} \left\{ g\left( x_1 \right) \right\} > \tan^{- 1} \left\{ g\left( x_2 \right) \right\}$

$\Rightarrow f\left( x_1 \right) > f\left( x_2 \right)$

$\text { Thus },$

$x_1 < x_2 \Rightarrow f\left( x_1 \right) > f\left( x_2 \right)$

$\text { So,}f\left( x \right)\text { is decreasing on R }.$

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Solution If G (X) is a Decreasing Function On R And F(X) = Tan−1 [G (X)]. State Whether F(X) is Increasing Or Decreasing On R ? Concept: Increasing and Decreasing Functions.
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