Find f(g(x)) f(x)=3x+9 , g(x)=5x-1(fog)x

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x - 1 (f o g) x)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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

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

Apply the distributive property.

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

Multiply $5$ by $3$ .

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

Multiply $- 1$ by $3$ .

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

Remove parentheses.

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

Step 4

Simplify the expression.

Move $o$ .

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

Reorder $15 x$ and $- 3 f g o x$ .

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