Find f(g(x)) f(x)=5x-6 , g(x)=4-4x

$f (x) = 5 x - 6$ , $g (x) = 4 - 4 x$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 - 4 x)$ by substituting in the value of $g$ into $f$ .

$f (4 - 4 x) = 5 (4 - 4 x) - 6$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 - 4 x) = 5 \cdot 4 + 5 (- 4 x) - 6$

Multiply $5$ by $4$ .

$f (4 - 4 x) = 20 + 5 (- 4 x) - 6$

Multiply $- 4$ by $5$ .

$f (4 - 4 x) = 20 - 20 x - 6$

Step 4

Subtract $6$ from $20$ .

$f (4 - 4 x) = - 20 x + 14$