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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)

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Answer:

  • check below!

given functions:

[tex]\sf f(x)=x^2+3x-7[/tex]

[tex]\sf g(x)=3x+5[/tex]

[tex]\sf h(x)=2x^2-4[/tex]

solving steps:

(a)

[tex]\sf f(g(x))[/tex]

[tex]\sf \sf f(3x+5)[/tex]

[tex]\sf (3x+5)^2 + 3(3x+5)-7[/tex]

[tex]\sf 9x^2+30x+25+9x+15-7[/tex]

[tex]\sf 9x^2+39x+33[/tex]

(b)

[tex]\sf h(g(x))[/tex]

[tex]\sf h(3x+5)[/tex]

[tex]\sf 2(3x+5)^2-4[/tex]

[tex]\sf 18x^2+60x+50-4[/tex]

[tex]\sf 18x^2+60x+46[/tex]

(c)

[tex]\sf (h-f)(x)[/tex]

[tex]\sf 2x^2-4-(x^2+3x-7)[/tex]

[tex]\sf 2x^2-4-x^2-3x+7[/tex]

[tex]\sf x^2-3x+3[/tex]

(d)

[tex]\sf (f+g)(x)[/tex]

[tex]\sf x^2 + 3x -7 +3x+5[/tex]

[tex]\sf x^2+6x-2[/tex]

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