Algebra Examples

$f (x) = 3 x + 9$ , $g (x) = 5 x - 1 (f o g) x$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x + 9)$ by substituting in the value of $f$ into $g$ .

$g (3 x + 9) = 5 (3 x + 9) - 1 (f o g) (3 x + 9)$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x + 9) = 5 (3 x) + 5 \cdot 9 - 1 (f o g) (3 x + 9)$

Step 3.2

Multiply $3$ by $5$ .

$g (3 x + 9) = 15 x + 5 \cdot 9 - 1 (f o g) (3 x + 9)$

Step 3.3

Multiply $5$ by $9$ .

$g (3 x + 9) = 15 x + 45 - 1 (f o g) (3 x + 9)$

Step 3.4

Rewrite $- 1 (f o g)$ as $- (f o g)$ .

$g (3 x + 9) = 15 x + 45 - f o g (3 x + 9)$

Step 3.5

Apply the distributive property.

$g (3 x + 9) = 15 x + 45 - f o g (3 x) - f o g \cdot 9$

Step 3.6

Multiply $3$ by $- 1$ .

$g (3 x + 9) = 15 x + 45 - 3 f o g x - f o g \cdot 9$

Step 3.7

Multiply $9$ by $- 1$ .

$g (3 x + 9) = 15 x + 45 - 3 f o g x - 9 f o g$

Step 4

Reorder.

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Step 4.1

Move $o$ .

$g (3 x + 9) = 15 x + 45 - 3 f g o x - 9 f o g$

Step 4.2

Move $o$ .

$g (3 x + 9) = 15 x + 45 - 3 f g o x - 9 f g o$

Step 4.3

Move $45$ .

$g (3 x + 9) = 15 x - 3 f g o x - 9 f g o + 45$

Step 4.4

Move $15 x$ .

$g (3 x + 9) = - 3 f g o x - 9 f g o + 15 x + 45$