Find f(g(x)) f(x)=9x-4 , g(x)=(x+9)/4

$f (x) = 9 x - 4$ , $g (x) = \frac{x + 9}{4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 9}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 9}{4}) = 9 (\frac{x + 9}{4}) - 4$

Step 3

Combine $9$ and $\frac{x + 9}{4}$ .

$f (\frac{x + 9}{4}) = \frac{9 (x + 9)}{4} - 4$

Step 4

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$f (\frac{x + 9}{4}) = \frac{9 (x + 9)}{4} - 4 \cdot \frac{4}{4}$

Step 5

Simplify terms.

Combine $- 4$ and $\frac{4}{4}$ .

$f (\frac{x + 9}{4}) = \frac{9 (x + 9)}{4} + \frac{- 4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$f (\frac{x + 9}{4}) = \frac{9 (x + 9) - 4 \cdot 4}{4}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 9}{4}) = \frac{9 x + 9 \cdot 9 - 4 \cdot 4}{4}$

Multiply $9$ by $9$ .

$f (\frac{x + 9}{4}) = \frac{9 x + 81 - 4 \cdot 4}{4}$

Multiply $- 4$ by $4$ .

$f (\frac{x + 9}{4}) = \frac{9 x + 81 - 16}{4}$

Subtract $16$ from $81$ .

$f (\frac{x + 9}{4}) = \frac{9 x + 65}{4}$