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
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