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

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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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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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