Question

Consider f:R→R given by f(x)=3x+2. Show that f is invertible. Find also the inverse of function f.

Answer 1

f(x) = 3x + 2

Let f(x₁​) = f(x₂​)

⇒ 3x₁ + 2 = 3x₂ + 2

⇒ x_1​ = x₂

Thus f is one-one

To check onto

let y = 3x + 2

⇒ x = \(\frac{y - 2}3\) here y ∈ R

Thus f(x) is onto

Thus f is invertible

Inverse of f is = \(\frac{x - 2}3\) = f^-1(x).