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

$f (x) = 2 x - 1$ , $g (x) = 3 x + 2$ , $h (x) = x^{2} (f (x) + g (x) + h (x))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x + 2)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $2$ .

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

Multiply $2$ by $2$ .

$f (3 x + 2) = 6 x + 4 - 1$

Step 4

Subtract $1$ from $4$ .

$f (3 x + 2) = 6 x + 3$