Precalculus Examples

$g (n) = 2 n + 3$ $h (n) = n - 1$ Find $((g \circ h)) (n)$

Step 1

Set up the composite result function.

$g (h (n))$

Step 2

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

$g (n - 1) = 2 (n - 1) + 3$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (n - 1) = 2 n + 2 \cdot - 1 + 3$

Step 3.2

Multiply $2$ by $- 1$ .

$g (n - 1) = 2 n - 2 + 3$

Step 4

Add $- 2$ and $3$ .

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