Solve the Function Operation f(x)=3x+5 , g(x)=x-1 , f(g(-3))

$f (x) = 3 x + 5$ , $g (x) = x - 1$ , $f (g (- 3))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x - 1)$ by substituting in the value of $g$ into $f$ .

$f (x - 1) = 3 (x - 1) + 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (x - 1) = 3 x + 3 \cdot - 1 + 5$

Multiply $3$ by $- 1$ .

$f (x - 1) = 3 x - 3 + 5$

Step 4

Add $- 3$ and $5$ .

$f (x - 1) = 3 x + 2$

Step 5

Evaluate the result function by replacing $x$ with $- 3$ in the function.

$3 (- 3) + 2$

Step 6

Simplify the evaluated function.

Multiply $3$ by $- 3$ .

$- 9 + 2$

Add $- 9$ and $2$ .

$- 7$