Find g(f(x)) f(x)=5x+15 , g(x)=5x-1

$f (x) = 5 x + 15$ , $g (x) = 5 x - 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (5 x + 15)$ by substituting in the value of $f$ into $g$ .

$g (5 x + 15) = 5 (5 x + 15) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$g (5 x + 15) = 5 (5 x) + 5 \cdot 15 - 1$

Multiply $5$ by $5$ .

$g (5 x + 15) = 25 x + 5 \cdot 15 - 1$

Multiply $5$ by $15$ .

$g (5 x + 15) = 25 x + 75 - 1$

Step 4

Subtract $1$ from $75$ .

$g (5 x + 15) = 25 x + 74$