#### Question

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

#### Solution

\[\text { Here }, \]

\[f\left( x \right) = 7x - 3\]

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

\[ x_1 < x_2 \]

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

\[ \Rightarrow 7 x_1 - 3 < 7 x_2 - 3\]

\[ \Rightarrow f\left( x_1 \right) < f\left( x_2 \right)\]

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

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

Is there an error in this question or solution?

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