The inverse function of f(x) is:
[tex]g(x) = \sqrt[3]{(x +1)/64}[/tex]
How to find the inverse function?
Here we have the function:
[tex]f(x) = 64*x^3 -1[/tex]
We want to find the inverse, we will say that is of the form:
[tex]g(x) = \sqrt[3]{a*x + b}[/tex]
If we evaluate f(x) on g(x), we get:
[tex]f(g(x)) = 64*(\sqrt[3]{ax + b})^3 - 1\\ \\f(g(x)) = 64*(ax + b) - 1[/tex]
If these are inverses, that must be equal to x:
[tex]64*(ax + b) - 1 = x\\\\64*a*x + 64*b - 1 = x\\[/tex]
Then:
64*a = 1
a = 1/64
64*b - 1 = 0
b = 1/64
So the inverse function is:
[tex]g(x) = \sqrt[3]{(x +1)/64}[/tex]
If you want to learn more about inverse functions:
https://brainly.com/question/14391067
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