Question

Find the inverse of the function

Answer 1

If h⁻¹(x) is the inverse of h(x), then by definition of inverse function,

h(h⁻¹(x)) = x

Given that h(x) = 6∛(2x + 5) - 1, we have

h(h⁻¹(x)) = 6∛(2 h⁻¹(x) + 5) - 1 = x

Solve for h⁻¹(x) :

6∛(2 h⁻¹(x) + 5) - 1 = x

6∛(2 h⁻¹(x) + 5) = x + 1

∛(2 h⁻¹(x) + 5) = (x + 1)/6

[∛(2 h⁻¹(x) + 5)]³ = [(x + 1)/6]³

2 h⁻¹(x) + 5 = (x + 1)³/216

2 h⁻¹(x) = (x + 1)³/216 - 5

h⁻¹(x) = (x + 1)³/432 - 5/2