Find g(f(x)) f(x)=x-7 , g(x)=x^3

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

Set up the composite result function.

$g (f (x))$

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

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

Use the Binomial Theorem.

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

Simplify each term.

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Multiply $- 7$ by $3$ .

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

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

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

Multiply $49$ by $3$ .

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

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

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

Find g(f(x)) f(x)=x-7 , g(x)=x^3

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