Precalculus Examples

$g (a) = 4 a + 1$ $h (a) = - 3 a + 2$ Find $g (h (1))$

Step 1

Set up the composite result function.

$g (h (a))$

Step 2

Evaluate $g (- 3 a + 2)$ by substituting in the value of $h$ into $g$ .

$g (- 3 a + 2) = 4 (- 3 a + 2) + 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (- 3 a + 2) = 4 (- 3 a) + 4 \cdot 2 + 1$

Step 3.2

Multiply $- 3$ by $4$ .

$g (- 3 a + 2) = - 12 a + 4 \cdot 2 + 1$

Step 3.3

Multiply $4$ by $2$ .

$g (- 3 a + 2) = - 12 a + 8 + 1$

Step 4

Add $8$ and $1$ .

$g (- 3 a + 2) = - 12 a + 9$

Step 5

Evaluate the result function by replacing $a$ with $1$ in the function.

$- 12 \cdot 1 + 9$

Step 6

Simplify the evaluated function.

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Step 6.1

Multiply $- 12$ by $1$ .

$- 12 + 9$

Step 6.2

Add $- 12$ and $9$ .

$- 3$