Precalculus Examples

$f (x) = 3 x - 1$ $g (x) = x^{2} - x - 4$ Find: $f (g (x))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} - x - 4)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} - x - 4) = 3 (x^{2} - x - 4) - 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{2} - x - 4) = 3 x^{2} + 3 (- x) + 3 \cdot - 4 - 1$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 1$ by $3$ .

$f (x^{2} - x - 4) = 3 x^{2} - 3 x + 3 \cdot - 4 - 1$

Step 3.2.2

Multiply $3$ by $- 4$ .

$f (x^{2} - x - 4) = 3 x^{2} - 3 x - 12 - 1$

Step 4

Subtract $1$ from $- 12$ .

$f (x^{2} - x - 4) = 3 x^{2} - 3 x - 13$