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# Solution for Prove that F(X) = Ax + B, Where A, B Are Constants and a < 0 is a Decreasing Function on R ? - CBSE (Commerce) Class 12 - Mathematics

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ConceptIncreasing and Decreasing Functions

#### Question

Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R ?

#### Solution

$f\left( x \right) = ax + b$

$\text { Let }x_1 , x_2 \text { in R such that } x_1 < x_2 .$

$\text { Then },$

$x_1 < x_2$

$\Rightarrow a x_1 > a x_2 (\because a<0)$

$\Rightarrow a x_1 + b > a x_2 + b$

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

$\text { Thus }, x_1 < x_2$

$\Rightarrow f\left( x_1 \right) > f\left( x_2 \right), \forall x_1 , x_2 \in R$

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

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Solution Prove that F(X) = Ax + B, Where A, B Are Constants and a < 0 is a Decreasing Function on R ? Concept: Increasing and Decreasing Functions.
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