Question

how do you find the inverse of f(x)=x^5 and graph it?

Answer 1

So basically set y = f(x),

so you get: y = x^5.
Then switch x and y, to get: x = y^5.

Now solve it for y again, and that's the inverse function. You can then graph it like any other function.

Answer 2

That's what i tried to do but my textbook says:

f(x)=x^5
x^5=y
x=sqrt 5 (y)
y=sqrt 5 (x)
f^-1(x)= sqrt 5(x)
f^-1(x)= x^(1/5)

How did the square root get there on the third equation?

Answer 3

Basically it's just the fifth root. So you know how you do this:

\[\sqrt[]{x^2} = x \rightarrow \sqrt[5]{x^5}=x\]

Answer 4

Great Thank you~