Question

Answer the following:

A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f^–1

Answer 1

f(x) = `(3x)/5 + 2`, x ∈ R

Let f(x₁) = f(x₂)

∴ `(3x_1)/5 + 2 = (3x_2)/5 + 2`

∴ x₁ = x₂

∴ f is a one-one function

Let f(x) = `(3x)/5 + 2` = y (say), y ∈ R

∴ x = `(5(y - 2))/3`

∴ for every y ∈ R, there is some x ∈ R

∴ f is an onto function.

x = `(5(y - 2))/3` = f^–1 (y)

∴ f^–1 (x) = `(5(x - 2))/3`