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

Therefore, the inverse of the function  f(x) = 3√(x/7) - 9 is 7(x + 9)3.

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