Find f(g(x)) f(x)=6x-4 , g(x)=(x+6)/4

$f (x) = 6 x - 4$ , $g (x) = \frac{x + 6}{4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 6}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 6}{4}) = 6 (\frac{x + 6}{4}) - 4$

Step 3

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$f (\frac{x + 6}{4}) = 2 (3) (\frac{x + 6}{4}) - 4$

Factor $2$ out of $4$ .

$f (\frac{x + 6}{4}) = 2 \cdot (3 (\frac{x + 6}{2 \cdot 2})) - 4$

Cancel the common factor.

$f (\frac{x + 6}{4}) = 2 \cdot (3 (\frac{x + 6}{2 \cdot 2})) - 4$

Rewrite the expression.

$f (\frac{x + 6}{4}) = 3 (\frac{x + 6}{2}) - 4$

Combine $3$ and $\frac{x + 6}{2}$ .

$f (\frac{x + 6}{4}) = \frac{3 (x + 6)}{2} - 4$

Step 4

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (\frac{x + 6}{4}) = \frac{3 (x + 6)}{2} - 4 \cdot \frac{2}{2}$

Step 5

Simplify terms.

Combine $- 4$ and $\frac{2}{2}$ .

$f (\frac{x + 6}{4}) = \frac{3 (x + 6)}{2} + \frac{- 4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$f (\frac{x + 6}{4}) = \frac{3 (x + 6) - 4 \cdot 2}{2}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 6}{4}) = \frac{3 x + 3 \cdot 6 - 4 \cdot 2}{2}$

Multiply $3$ by $6$ .

$f (\frac{x + 6}{4}) = \frac{3 x + 18 - 4 \cdot 2}{2}$

Multiply $- 4$ by $2$ .

$f (\frac{x + 6}{4}) = \frac{3 x + 18 - 8}{2}$

Subtract $8$ from $18$ .

$f (\frac{x + 6}{4}) = \frac{3 x + 10}{2}$