Algebra Examples

$f (x) = \sqrt[3]{\frac{x - 3}{7}}$ , $g (x) = 7 x^{3} + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (7 x^{3} + 3)$ by substituting in the value of $g$ into $f$ .

$f (7 x^{3} + 3) = \sqrt[3]{\frac{(7 x^{3} + 3) - 3}{7}}$

Step 3

Subtract $3$ from $3$ .

$f (7 x^{3} + 3) = \sqrt[3]{\frac{7 x^{3} + 0}{7}}$

Step 4

Add $7 x^{3}$ and $0$ .

$f (7 x^{3} + 3) = \sqrt[3]{\frac{7 x^{3}}{7}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Reduce the expression $\frac{7 x^{3}}{7}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

$f (7 x^{3} + 3) = \sqrt[3]{\frac{7 x^{3}}{7}}$

Step 5.1.2

Rewrite the expression.

$f (7 x^{3} + 3) = \sqrt[3]{\frac{x^{3}}{1}}$

Step 5.2

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

$f (7 x^{3} + 3) = \sqrt[3]{x^{3}}$

Step 6

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

$f (7 x^{3} + 3) = x$