PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for Prove that F(X) = Ax + B, Where A, B Are Constants and a > 0 is an Increasing Function on R ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

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

#### Solution

$\text { Here },$

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

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

$x_1 < x_2$

$\Rightarrow a x_1 < a x_2 \left[ \because a>0 \right]$

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

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

$\therefore x_1 < x_2$

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

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

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#### Video TutorialsVIEW ALL [3]

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