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 decreasing function on R.

✓

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)

Thus, 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 decreasing on R.

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