Find f(g(x)) f(x)=3x-7 , g(x)=x-6

$f (x) = 3 x - 7$ , $g (x) = x - 6$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x - 6)$ by substituting in the value of $g$ into $f$ .

$f (x - 6) = 3 (x - 6) - 7$

Step 3

Simplify each term.

Apply the distributive property.

$f (x - 6) = 3 x + 3 \cdot - 6 - 7$

Multiply $3$ by $- 6$ .

$f (x - 6) = 3 x - 18 - 7$

Step 4

Subtract $7$ from $- 18$ .

$f (x - 6) = 3 x - 25$