Find g(f(x)) f(x)=x+5 , g(x)=x^3+125

$f (x) = x + 5$ , $g (x) = x^{3} + 125$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (x + 5) = {(x + 5)}^{3} + 125$

Step 3

Simplify each term.

Use the Binomial Theorem.

$g (x + 5) = x^{3} + 3 x^{2} \cdot 5 + 3 x \cdot 5^{2} + 5^{3} + 125$

Simplify each term.

Multiply $5$ by $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 3 x \cdot 5^{2} + 5^{3} + 125$

Raise $5$ to the power of $2$ .

$g (x + 5) = x^{3} + 15 x^{2} + 3 x \cdot 25 + 5^{3} + 125$

Multiply $25$ by $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 5^{3} + 125$

Raise $5$ to the power of $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 125 + 125$

Step 4

Add $125$ and $125$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 250$