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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Subtract $3$ from $3$ .

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

Step 4

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

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

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.

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

Rewrite the expression.

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

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

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

Step 6

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

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