For the function g(x) =10 x ^5/x-2, what is the inverse function?

Question

asked Jan 8, 2022 187k views

1 Answer

Jrsm · Answer 1 · 2022-01-14T16:48:38+0000

Answer:

g^(-1)(x) =((x)/(10))^(5) +2

Explanation:

So we have the function
$g(x)=10\sqrt[5]{x-2}$ . To find the inverse, we first set the function equal to y:

$y=10\sqrt[5]{x-2}$

Then, we switch all the y and x variables, like this:

$x=10\sqrt[5]{y-2}$

Now, we solve for y to find the inverse function:

$x=10\sqrt[5]{y-2}$

$(x)/(10) =\sqrt[5]{y-2}$

((x)/(10))^(5) =y-2

((x)/(10))^(5) +2=y

y=((x)/(10))^(5) +2

g^(-1)(x) =((x)/(10))^(5) +2