Find f(g(x)) f(x)=5x-9 g(x)=(x+5)/9

$f (x) = 5 x - 9$ $g (x) = \frac{x + 5}{9}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 5}{9})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 5}{9}) = 5 (\frac{x + 5}{9}) - 9$

Step 3

Combine $5$ and $\frac{x + 5}{9}$ .

$f (\frac{x + 5}{9}) = \frac{5 (x + 5)}{9} - 9$

Step 4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$f (\frac{x + 5}{9}) = \frac{5 (x + 5)}{9} - 9 \cdot \frac{9}{9}$

Step 5

Simplify terms.

Combine $- 9$ and $\frac{9}{9}$ .

$f (\frac{x + 5}{9}) = \frac{5 (x + 5)}{9} + \frac{- 9 \cdot 9}{9}$

Combine the numerators over the common denominator.

$f (\frac{x + 5}{9}) = \frac{5 (x + 5) - 9 \cdot 9}{9}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 5}{9}) = \frac{5 x + 5 \cdot 5 - 9 \cdot 9}{9}$

Multiply $5$ by $5$ .

$f (\frac{x + 5}{9}) = \frac{5 x + 25 - 9 \cdot 9}{9}$

Multiply $- 9$ by $9$ .

$f (\frac{x + 5}{9}) = \frac{5 x + 25 - 81}{9}$

Subtract $81$ from $25$ .

$f (\frac{x + 5}{9}) = \frac{5 x - 56}{9}$