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Help pleas Given that f(x)=x^2+3x−7, g(x)=3x+5, and h(x)=2x^2−4, find each of the following. Solve each of the problems showing work.

f(g(x))
h(g(x))
(h−f)(x)
(f+g)(x)

1 Answer

9 votes

Answer:

  • check below!

given functions:


\sf f(x)=x^2+3x-7


\sf g(x)=3x+5


\sf h(x)=2x^2-4

solving steps:

(a)


\sf f(g(x))


\sf \sf f(3x+5)


\sf (3x+5)^2 + 3(3x+5)-7


\sf 9x^2+30x+25+9x+15-7


\sf 9x^2+39x+33

(b)


\sf h(g(x))


\sf h(3x+5)


\sf 2(3x+5)^2-4


\sf 18x^2+60x+50-4


\sf 18x^2+60x+46

(c)


\sf (h-f)(x)


\sf 2x^2-4-(x^2+3x-7)


\sf 2x^2-4-x^2-3x+7


\sf x^2-3x+3

(d)


\sf (f+g)(x)


\sf x^2 + 3x -7 +3x+5


\sf x^2+6x-2

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