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# Solution for Without Using the Derivative Show that the Function F (X) = 7x − 3 is Strictly Increasing Function on R ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Without using the derivative show that the function f (x) = 7x − 3 is strictly increasing function on R ?

#### Solution

$\text { Here },$

$f\left( x \right) = 7x - 3$

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

$x_1 < x_2$

$\Rightarrow 7 x_1 < 7 x_2 \left[ \because 7 >0 \right]$

$\Rightarrow 7 x_1 - 3 < 7 x_2 - 3$

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

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

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

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Solution Without Using the Derivative Show that the Function F (X) = 7x − 3 is Strictly Increasing Function on R ? Concept: Increasing and Decreasing Functions.
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