Question

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

Answer 1

$$\begin{gathered} \mathrm{Here}, \\ f\left(x\right)=7x-3 \\ \text{Let}{x}_1,x_2\in R\text{such that}{x}_1<x_2.\text{Then,} \\ {x}_1<x_2 \\ \Rightarrow 7x_1<7x_2\left[\text{∵ 7 >0}\right] \\ \Rightarrow 7x_1-3<7x_2-3 \\ \Rightarrow f\left(x_1\right)<f\left(x_2\right) \\ \text{∴}{x}_1<x_2\Rightarrow f\left(x_1\right)<f\left(x_2\right),\forall x_1,x_2\in R \\ \text{So,}f\left(x\right)\text{is strictly increasing on}R. \end{gathered}$$