Find f(g(x)) f(x)=3x-5 , g(x)=2x+1

$f (x) = 3 x - 5$ , $g (x) = 2 x + 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x + 1)$ by substituting in the value of $g$ into $f$ .

$f (2 x + 1) = 3 (2 x + 1) - 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x + 1) = 3 (2 x) + 3 \cdot 1 - 5$

Multiply $2$ by $3$ .

$f (2 x + 1) = 6 x + 3 \cdot 1 - 5$

Multiply $3$ by $1$ .

$f (2 x + 1) = 6 x + 3 - 5$

Step 4

Subtract $5$ from $3$ .

$f (2 x + 1) = 6 x - 2$