Find f(g(x)) f(x)=4x+11 , g(x)=2x-1

$f (x) = 4 x + 11$ , $g (x) = 2 x - 1$

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 $f$ .

$f (2 x - 1) = 4 (2 x - 1) + 11$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x - 1) = 4 (2 x) + 4 \cdot - 1 + 11$

Multiply $2$ by $4$ .

$f (2 x - 1) = 8 x + 4 \cdot - 1 + 11$

Multiply $4$ by $- 1$ .

$f (2 x - 1) = 8 x - 4 + 11$

Step 4

Add $- 4$ and $11$ .

$f (2 x - 1) = 8 x + 7$