Question

If f :R → R is a function defined by f(x) = 3x – 2

1. Show that f is one-one.

2. Find fof(x).

3. Find the inverse of f if exists.

Answer 1

1. f(x₁) = f(x₂)
⇒ 2x₁ – 3 = 2x₂ – 3 ⇒ x₁ = x₂
Therefore one-one.

2. fof(x) = f(f(x)) = f(3x – 2)
f (x) = 3(3x – 2) – 2 = 9x – 6 – 2 = 9x – 8.

3. Let g(x) = \(\frac{x+2}{3}\)

fog(x) = f(g(x))

= f\((\frac{x+2}{3})\) = 3\((\frac{x+2}{3})\) - 2 = x

Similarly we can show that
gof(x) = g(f(x)) = x

Therefore; f^-1 = \((\frac{x+2}{3})\)