Question

1. Consider f: {3, 4, 5, 6} → {8, 10, 12, 13, 14} And f = { (3, 8), (4, 10), (5, 12), (6, 14)}. State whether f has inverse ? Give reason. 

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

Answer 1

1. Distinct elements in set {3, 4, 5, 6} has distinct images, under f.

∴ f is one- one

But 14 in the codomain has no pre image.

∴ f is not onto.

∴ f has no inverse.

2. f(x) = 3x + 2; then

f(x₁) = f(x₂) = 3x₂ + 2 ⇒ x₁= x₂

Hence F is one – one

For y ∈ R, let y = 3x + 2 ⇒ x = \(\frac{y-2}{3}∈ R\)