Question

Find the inverse of the function f(x) = 9x^3 + 2

the inverse of f is g(x)

Answer 1

g(x) = 1/3 ∛(3(x - 2))

Explanation:

f(x) = 9x³ + 2

interchange the variables:

x = 9y³ + 2

Solve for y:

9y³ = x - 2

y³ = (x - 2)/9

y = ∛((x - 2)/9)

y = ∛((x - 2)/9) · 3/3 = ∛(3(x - 2) / 27) = ∛(3(x - 2)) / 3 **multiply by 3/3 to simplify the radical

g(x) = 1/3 ∛(3(x - 2))

Answer 2

rewrite as x = 9y^3 + 2. Then solve for y