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

Question

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

Philoid · Accepted Answer

we have,

f(x) = ax + b, a > 0

let x₁,x₂ R and x₁ > x₂

⇒ ax₁ > ax₂ for some a > 0

⇒ ax₁ + b> ax₂ + b for some b

⇒ f(x₁) > f(x₂)

Hence, x₁ > x₂⇒ f(x₁) > f(x₂)

So, f(x) is increasing function of R