Question

Let f(x) = 4 − (x − 7)³ be an invertible function, then find f⁻¹(x).

Answer 1

F(x) = 4 − (x − 7)³    ...[Set y = f(x)]

Let y = 4 − (x − 7)³

(x − 7)³ = 4 − y    ...[Rearranging the terms]

x − 7 = `(4 − y)^(1/3)`    ...[Taking cube root]

x = 7 + `(4 − y)^(1/3)` 

Since f(x) = y ⇒ x = f⁻¹(y),

f⁻¹(y) = 7 + `(4 − y)^(1/3)`   ...[Replace y with x to get]

f⁻¹ (x) = 7 + `(4 − x)^(1/3)`