Question

Find the inverse function of f.
f(x)= x^7

Answer 1

I have no idea how to solve for this. That's all the question says.

Answer 2

x^7 = x*x*x*x*x*x*x, so the inverse is the 7th root of x

Answer 3

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 4

I'm probably just making it harder than it is. So the answer would be
f^-1=x^-7
?

Answer 5

Nope, lets do this step by step.

Answer 6

\[f(x)=x^7 \implies y=x^7\]

\[x=y^7\]
interchange x and y's, now solve for y.

\[\large \sqrt[7]{x} = \sqrt[7]{(y^7)} \implies y = \sqrt[7]{x} \implies f^{-1}(x) = \sqrt[7]{x}\]