# Find the inverse of the function f(x) = [cube root x/7] - 9

An inverse function is the reverse of an original function.

## Answer: The Inverse of the function f(x) = [cube root x/7] - 9 is 7 (x + 9)^{3}.

Let us proceed step by step

**Explanation:**

From the given function

f(x) = ^{3}**√**(x/7) - 9

on replacing f(x) with y we get,

y = ^{3}**√**(x/7) - 9

Since we are finding the inverse so we need to interchange the variables.

Therefore, x = ^{3}**√ **(y/7) - 9

Let us simplify the given equation further, we get

x + 9 = ^{3}**√**(y/7)

(x + 9)^{3} = y/7 [ On taking cube to the both sides ]

7 (x + 9)^{3} = y

Replacing y with f^{-1}(x), we get

f^{-1}(x) = 7 (x + 9)^{3}