Find f(g(x)) f(x) = cube root of (x-2)/5 , g(x)=5x^3+2

$f (x) = \sqrt[3]{\frac{x - 2}{5}}$ , $g (x) = 5 x^{3} + 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x^{3} + 2)$ by substituting in the value of $g$ into $f$ .

$f (5 x^{3} + 2) = \sqrt[3]{\frac{(5 x^{3} + 2) - 2}{5}}$

Step 3

Subtract $2$ from $2$ .

$f (5 x^{3} + 2) = \sqrt[3]{\frac{5 x^{3} + 0}{5}}$

Step 4

Add $5 x^{3}$ and $0$ .

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

Step 5

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{5 x^{3}}{5}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$f (5 x^{3} + 2) = \sqrt[3]{\frac{x^{3}}{1}}$

Divide $x^{3}$ by $1$ .

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

Step 6

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

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