Precalculus Examples

$g (n) = 3 n + 2$ $f (n) = 2 n^{2} + 5$ Find $g (f (2))$

Step 1

Set up the composite result function.

$g (f (n))$

Step 2

Evaluate $g (2 n^{2} + 5)$ by substituting in the value of $f$ into $g$ .

$g (2 n^{2} + 5) = 3 (2 n^{2} + 5) + 2$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $2$ by $3$ .

$g (2 n^{2} + 5) = 6 n^{2} + 3 \cdot 5 + 2$

Step 3.3

Multiply $3$ by $5$ .

$g (2 n^{2} + 5) = 6 n^{2} + 15 + 2$

Step 4

Add $15$ and $2$ .

$g (2 n^{2} + 5) = 6 n^{2} + 17$

Step 5

Evaluate the result function by replacing $n$ with $2$ in the function.

$6 {(2)}^{2} + 17$

Step 6

Simplify the evaluated function.

Tap for more steps...

Step 6.1

Simplify each term.

Tap for more steps...

Step 6.1.1

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

$6 \cdot 4 + 17$

Step 6.1.2

Multiply $6$ by $4$ .

$24 + 17$

Step 6.2

Add $24$ and $17$ .

$41$