Algebra Examples

$f (x) = x - 7$ , $g (x) = x^{3}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x - 7)$ by substituting in the value of $f$ into $g$ .

$g (x - 7) = {(x - 7)}^{3}$

Step 3

Use the Binomial Theorem.

$g (x - 7) = x^{3} + 3 x^{2} \cdot - 7 + 3 x {(- 7)}^{2} + {(- 7)}^{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 7$ by $3$ .

$g (x - 7) = x^{3} - 21 x^{2} + 3 x {(- 7)}^{2} + {(- 7)}^{3}$

Step 4.2

Raise $- 7$ to the power of $2$ .

$g (x - 7) = x^{3} - 21 x^{2} + 3 x \cdot 49 + {(- 7)}^{3}$

Step 4.3

Multiply $49$ by $3$ .

$g (x - 7) = x^{3} - 21 x^{2} + 147 x + {(- 7)}^{3}$

Step 4.4

Raise $- 7$ to the power of $3$ .

$g (x - 7) = x^{3} - 21 x^{2} + 147 x - 343$