Find f(g(x)) f(x)=4x-5 , g(x)=6x-3

$f (x) = 4 x - 5$ , $g (x) = 6 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (6 x - 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $6$ by $4$ .

$f (6 x - 3) = 24 x + 4 \cdot - 3 - 5$

Multiply $4$ by $- 3$ .

$f (6 x - 3) = 24 x - 12 - 5$

Step 4

Subtract $5$ from $- 12$ .

$f (6 x - 3) = 24 x - 17$