Question

Find the inverse of the function: a, b ∈ R, f : R → R defined by f(x) = ax + b (a ≠ 0)

Answer 1

Given ,

a, b ∈ R, f : R → R defined by

f(x) = ax + b (a ≠ 0)

Let f(x) = y .

y = ax + b

y - b = ax

y - b / a = x

x = y - b / a.

So, f'(y) = y - b / a

f'(x) = x - b/a

Therefore, The inverse function of f(x) is f'(x) = x - b / a, a ≠ 0 .