Find f(g(x)) f(x)=7x-4 , g(x)=(x+7)/4

$f (x) = 7 x - 4$ , $g (x) = \frac{x + 7}{4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 7}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 7}{4}) = 7 (\frac{x + 7}{4}) - 4$

Step 3

Combine $7$ and $\frac{x + 7}{4}$ .

$f (\frac{x + 7}{4}) = \frac{7 (x + 7)}{4} - 4$

Step 4

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

$f (\frac{x + 7}{4}) = \frac{7 (x + 7)}{4} - 4 \cdot \frac{4}{4}$

Step 5

Simplify terms.

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

$f (\frac{x + 7}{4}) = \frac{7 (x + 7)}{4} + \frac{- 4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$f (\frac{x + 7}{4}) = \frac{7 (x + 7) - 4 \cdot 4}{4}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 7}{4}) = \frac{7 x + 7 \cdot 7 - 4 \cdot 4}{4}$

Multiply $7$ by $7$ .

$f (\frac{x + 7}{4}) = \frac{7 x + 49 - 4 \cdot 4}{4}$

Multiply $- 4$ by $4$ .

$f (\frac{x + 7}{4}) = \frac{7 x + 49 - 16}{4}$

Subtract $16$ from $49$ .

$f (\frac{x + 7}{4}) = \frac{7 x + 33}{4}$