Precalculus Examples

$f (x) = 3 x + 10$ $g (x) = x - 2$ find $f (g (5))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x - 2)$ by substituting in the value of $g$ into $f$ .

$f (x - 2) = 3 (x - 2) + 10$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x - 2) = 3 x + 3 \cdot - 2 + 10$

Step 3.2

Multiply $3$ by $- 2$ .

$f (x - 2) = 3 x - 6 + 10$

Step 4

Add $- 6$ and $10$ .

$f (x - 2) = 3 x + 4$

Step 5

Evaluate the result function by replacing $x$ with $5$ in the function.

$3 (5) + 4$

Step 6

Simplify the evaluated function.

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Step 6.1

Multiply $3$ by $5$ .

$15 + 4$

Step 6.2

Add $15$ and $4$ .

$19$