23) (h(x)=-3x^{2}+5) (g(x)=3x + 2) find (h(g(x)))

Explanation:

Step1: Substitute g(x) into h(x)

$h(g(x))=-3(3x + 2)^2+5$

Step2: Expand $(3x + 2)^2$

$(3x + 2)^2=(3x + 2)(3x + 2)=9x^2+12x + 4$

Step3: Multiply by -3 and add 5

$h(g(x))=-3(9x^2+12x + 4)+5=-27x^2-36x-12 + 5=-27x^2-36x-7$

Answer:

$-27x^2-36x - 7$