Show that the function given by f(x) = 7x – 3 is increasing on R. - Vidyadip

Question

Show that the function given by $f(x) = 7x – 3$ is increasing on $R$.

✓

Answer

Let $x_1$ and $x_2$ be any two numbers in $R$. Then
$\mathrm{x}_1<\mathrm{x}_2$
$\Rightarrow 7 \mathrm{x}_1<7 \mathrm{x}_2$
$\Rightarrow 7 \mathrm{x}_1-3<7 \mathrm{x}_2-3$
$\Rightarrow \mathrm{f}\left(\mathrm{x}_1\right)<\mathrm{f}\left(\mathrm{x}_2\right)$
Thus, f is strictly increasing on $R$.

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