Precalculus Examples

$f (x) = 3 x - 7$ and $g (x) = - 2 x - 6$ Find $((f \circ g)) (4)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 2 x - 6)$ by substituting in the value of $g$ into $f$ .

$f (- 2 x - 6) = 3 (- 2 x - 6) - 7$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (- 2 x - 6) = 3 (- 2 x) + 3 \cdot - 6 - 7$

Step 3.2

Multiply $- 2$ by $3$ .

$f (- 2 x - 6) = - 6 x + 3 \cdot - 6 - 7$

Step 3.3

Multiply $3$ by $- 6$ .

$f (- 2 x - 6) = - 6 x - 18 - 7$

Step 4

Subtract $7$ from $- 18$ .

$f (- 2 x - 6) = - 6 x - 25$

Step 5

Evaluate the result function by replacing $x$ with $4$ in the function.

$- 6 \cdot 4 - 25$

Step 6

Simplify the evaluated function.

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Step 6.1

Multiply $- 6$ by $4$ .

$- 24 - 25$

Step 6.2

Subtract $25$ from $- 24$ .

$- 49$