Find f(g(x)) f(x)=2x-5 , g(x)=4x+3

$f (x) = 2 x - 5$ , $g (x) = 4 x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x + 3)$ by substituting in the value of $g$ into $f$ .

$f (4 x + 3) = 2 (4 x + 3) - 5$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x + 3) = 2 (4 x) + 2 \cdot 3 - 5$

Multiply $4$ by $2$ .

$f (4 x + 3) = 8 x + 2 \cdot 3 - 5$

Multiply $2$ by $3$ .

$f (4 x + 3) = 8 x + 6 - 5$

Step 4

Subtract $5$ from $6$ .

$f (4 x + 3) = 8 x + 1$