Find h(f(x)) f(x)=8x^3+5 h(x) = cube root of x-5

$f (x) = 8 x^{3} + 5$ $h (x) = \sqrt[3]{x - 5}$

Set up the composite result function.

$h (f (x))$

Evaluate $h (8 x^{3} + 5)$ by substituting in the value of $f$ into $h$ .

$h (8 x^{3} + 5) = \sqrt[3]{(8 x^{3} + 5) - 5}$

Simplify by subtracting numbers.

Subtract $5$ from $5$ .

$h (8 x^{3} + 5) = \sqrt[3]{8 x^{3} + 0}$

Add $8 x^{3}$ and $0$ .

$h (8 x^{3} + 5) = \sqrt[3]{8 x^{3}}$

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

$h (8 x^{3} + 5) = \sqrt[3]{{(2 x)}^{3}}$

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

$h (8 x^{3} + 5) = 2 x$