Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (5 x - 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $5$ .

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

Multiply $5$ by $- 1$ .

$f (5 x - 1) = 25 x - 5 + 15$

Step 4

Add $- 5$ and $15$ .

$f (5 x - 1) = 25 x + 10$