Prove that f(x) = ax + b, where a, b are constants and a > 0 is a… - Vidyadip

Question

Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R.

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Answer

Here,
f(x) = ax + b
Let $\text{x}_1,\text{x}_2\in\text{R}$ such that x₁< x₂. Then,
x₁< x₂
⇒ ax₁ < ax₂$[\because\ \text{a}>0]$
⇒ ax₁ + b < ax₂ + b
⇒ f(x₁) < f(x₂)
$\therefore$ x₁ < x₂
$\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2),\forall\text{x}_1,\text{x}_2\in\text{R}$
So, f(x) is increasing on R.

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