What is the inverse of y=x^(1/5)+1 ?

Mar 13, 2018

the inverse function of $y = {x}^{\frac{1}{5}} + 1$ is $y = {\left(x - 1\right)}^{5}$

Explanation:

When solving for the inverse of a function, you try to solve for x. If you plug in some number into a function it should give you only one output. What the inverse does is take that output and give you what you inputted into the first function. So solving for the "x" of a function will "undo" the alteration the original function did to the input. Solving for "x" goes as follows:

$y = {x}^{\frac{1}{5}} + 1$,

$y - 1 = {x}^{\frac{1}{5}}$,

${\left(y - 1\right)}^{5} = {\left({x}^{\frac{1}{5}}\right)}^{5}$,

${\left(y - 1\right)}^{5} = x$

Now finally swap the x and the y to get the function in a form that can be "understood."

${\left(x - 1\right)}^{5} = y$

Therefore the inverse function of $y = {x}^{\frac{1}{5}} + 1$ is $y = {\left(x - 1\right)}^{5}$