Given f(x) = 3x - 2 for all x in R Prove that f is one-to-one.

Question

Given f(x) = 3x - 2 for all x R

Prove that f is one-to-one.  

Answer 1

Proof.

Suppose f(x₁) = f(x₂) for x₁,x₂ ∈ R. Then

3x₁ − 2 = 3x₂ − 2 (Add 2 to both sides)

3x₁ = 3x₂ (Divide both sides by 3)

x₁ = x₂

Therefore, f is one-to-one on R.