Precalculus Examples

$f (x) = x + 7$ $g (x) = x^{2} + 2 x - 1$ Find: $g (f (x))$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x + 7)$ by substituting in the value of $f$ into $g$ .

$g (x + 7) = {(x + 7)}^{2} + 2 (x + 7) - 1$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Rewrite ${(x + 7)}^{2}$ as $(x + 7) (x + 7)$ .

$g (x + 7) = (x + 7) (x + 7) + 2 (x + 7) - 1$

Step 3.2

Expand $(x + 7) (x + 7)$ using the FOIL Method.

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$g (x + 7) = x (x + 7) + 7 (x + 7) + 2 (x + 7) - 1$

Step 3.2.2

Apply the distributive property.

$g (x + 7) = x \cdot x + x \cdot 7 + 7 (x + 7) + 2 (x + 7) - 1$

Step 3.2.3

Apply the distributive property.

$g (x + 7) = x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Step 3.3

Simplify and combine like terms.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Multiply $x$ by $x$ .

$g (x + 7) = x^{2} + x \cdot 7 + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Step 3.3.1.2

Move $7$ to the left of $x$ .

$g (x + 7) = x^{2} + 7 \cdot x + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Step 3.3.1.3

Multiply $7$ by $7$ .

$g (x + 7) = x^{2} + 7 x + 7 x + 49 + 2 (x + 7) - 1$

Step 3.3.2

Add $7 x$ and $7 x$ .

$g (x + 7) = x^{2} + 14 x + 49 + 2 (x + 7) - 1$

Step 3.4

Apply the distributive property.

$g (x + 7) = x^{2} + 14 x + 49 + 2 x + 2 \cdot 7 - 1$

Step 3.5

Multiply $2$ by $7$ .

$g (x + 7) = x^{2} + 14 x + 49 + 2 x + 14 - 1$

Step 4

Simplify by adding terms.

Tap for more steps...

Step 4.1

Add $14 x$ and $2 x$ .

$g (x + 7) = x^{2} + 16 x + 49 + 14 - 1$

Step 4.2

Simplify by adding and subtracting.

Tap for more steps...

Step 4.2.1

Add $49$ and $14$ .

$g (x + 7) = x^{2} + 16 x + 63 - 1$

Step 4.2.2

Subtract $1$ from $63$ .

$g (x + 7) = x^{2} + 16 x + 62$