Find f(g(x)) f(x)=2x^3+2x-3 g(x)=-0.5|x-4|

$f (x) = 2 x^{3} + 2 x - 3$ $g (x) = - 0.5 | x - 4 |$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 0.5 | x - 4 |)$ by substituting in the value of $g$ into $f$ .

$f (- 0.5 | x - 4 |) = 2 {(- 0.5 | x - 4 |)}^{3} + 2 (- 0.5 | x - 4 |) - 3$

Step 3

Simplify each term.

Apply the product rule to $- 0.5 | x - 4 |$ .

$f (- 0.5 | x - 4 |) = 2 ({(- 0.5)}^{3} {| x - 4 |}^{3}) + 2 (- 0.5 | x - 4 |) - 3$

Raise $- 0.5$ to the power of $3$ .

$f (- 0.5 | x - 4 |) = 2 (- 0.125 {| x - 4 |}^{3}) + 2 (- 0.5 | x - 4 |) - 3$

Multiply $- 0.125$ by $2$ .

$f (- 0.5 | x - 4 |) = - 0.25 {| x - 4 |}^{3} + 2 (- 0.5 | x - 4 |) - 3$

Multiply $- 0.5$ by $2$ .

$f (- 0.5 | x - 4 |) = - 0.25 {| x - 4 |}^{3} - 1 | x - 4 | - 3$

Rewrite $- 1 | x - 4 |$ as $- | x - 4 |$ .

$f (- 0.5 | x - 4 |) = - 0.25 {| x - 4 |}^{3} - | x - 4 | - 3$