Precalculus Examples

$f (x) = - 3 x + 1$ $g (x) = 3 x^{2} + 4 x - 15$ Find: $f (g (x))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x^{2} + 4 x - 15)$ by substituting in the value of $g$ into $f$ .

$f (3 x^{2} + 4 x - 15) = - 3 (3 x^{2} + 4 x - 15) + 1$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the distributive property.

$f (3 x^{2} + 4 x - 15) = - 3 (3 x^{2}) - 3 (4 x) - 3 \cdot - 15 + 1$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Multiply $3$ by $- 3$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 3 (4 x) - 3 \cdot - 15 + 1$

Step 3.2.2

Multiply $4$ by $- 3$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x - 3 \cdot - 15 + 1$

Step 3.2.3

Multiply $- 3$ by $- 15$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x + 45 + 1$

Step 4

Add $45$ and $1$ .

$f (3 x^{2} + 4 x - 15) = - 9 x^{2} - 12 x + 46$