Precalculus Examples

$g (n) = 4 n - 5$ $h (n) = 2 n + 1$ Find $g (h (8))$

Step 1

Set up the composite result function.

$g (h (n))$

Step 2

Evaluate $g (2 n + 1)$ by substituting in the value of $h$ into $g$ .

$g (2 n + 1) = 4 (2 n + 1) - 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (2 n + 1) = 4 (2 n) + 4 \cdot 1 - 5$

Step 3.2

Multiply $2$ by $4$ .

$g (2 n + 1) = 8 n + 4 \cdot 1 - 5$

Step 3.3

Multiply $4$ by $1$ .

$g (2 n + 1) = 8 n + 4 - 5$

Step 4

Subtract $5$ from $4$ .

$g (2 n + 1) = 8 n - 1$

Step 5

Evaluate the result function by replacing $n$ with $8$ in the function.

$8 (8) - 1$

Step 6

Simplify the evaluated function.

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Step 6.1

Multiply $8$ by $8$ .

$64 - 1$

Step 6.2

Subtract $1$ from $64$ .

$63$