Question

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)

Answer 1

• 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`