Prove that f(x) = ax + b, where a, b are constants and a

Question

Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing 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 decreasing function of R