Find f(g(x)) f(x)=3x-7 and g(x)=(x+3)/7

$f (x) = 3 x - 7$ and $g (x) = \frac{x + 3}{7}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 3}{7})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 3}{7}) = 3 (\frac{x + 3}{7}) - 7$

Step 3

Combine $3$ and $\frac{x + 3}{7}$ .

$f (\frac{x + 3}{7}) = \frac{3 (x + 3)}{7} - 7$

Step 4

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f (\frac{x + 3}{7}) = \frac{3 (x + 3)}{7} - 7 \cdot \frac{7}{7}$

Step 5

Simplify terms.

Combine $- 7$ and $\frac{7}{7}$ .

$f (\frac{x + 3}{7}) = \frac{3 (x + 3)}{7} + \frac{- 7 \cdot 7}{7}$

Combine the numerators over the common denominator.

$f (\frac{x + 3}{7}) = \frac{3 (x + 3) - 7 \cdot 7}{7}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 3}{7}) = \frac{3 x + 3 \cdot 3 - 7 \cdot 7}{7}$

Multiply $3$ by $3$ .

$f (\frac{x + 3}{7}) = \frac{3 x + 9 - 7 \cdot 7}{7}$

Multiply $- 7$ by $7$ .

$f (\frac{x + 3}{7}) = \frac{3 x + 9 - 49}{7}$

Subtract $49$ from $9$ .

$f (\frac{x + 3}{7}) = \frac{3 x - 40}{7}$