Find f(g(x)) f(x) = fifth root of x-5 , g(x)=x^5+5

$f (x) = \sqrt[5]{x - 5}$ , $g (x) = x^{5} + 5$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{5} + 5)$ by substituting in the value of $g$ into $f$ .

$f (x^{5} + 5) = \sqrt[5]{(x^{5} + 5) - 5}$

Step 3

Subtract $5$ from $5$ .

$f (x^{5} + 5) = \sqrt[5]{x^{5} + 0}$

Step 4

Add $x^{5}$ and $0$ .

$f (x^{5} + 5) = \sqrt[5]{x^{5}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$f (x^{5} + 5) = x$