Question

LaTeX: h\left(x\right)=x^3-3x^2+2xh ( x ) = x 3 − 3 x 2 + 2 x

LaTeX: g\left(x\right)=2x+3g ( x ) = 2 x + 3
Find LaTeX: \left(h+g\right)( h + g )(-8)

Answer 1

To find (h+g)(-8), calculate h(-8) and g(-8) by substituting -8 into the functions h(x) and g(x), then add the results to get -733.

Step-by-step explanation:

To find (h+g)(-8), we first need to determine the individual functions h(x) and g(x) at x=-8 and then add the results together. The function h(x) = x^3 - 3x^2 + 2x and g(x) = 2x + 3. Thus, we calculate:

• h(-8) = (-8)^3 - 3(-8)^2 + 2(-8) = -512 - 3(64) - 16 = -512 - 192 - 16 = -720
• g(-8) = 2(-8) + 3 = -16 + 3 = -13

Adding these results together:

(h+g)(-8) = h(-8) + g(-8) = -720 + (-13) = -733

The value of (h+g)(-8) is -733.