SOLUTION: Use the functions f(x) = 2x +7, g(x) = x squared + 3x, and h(x) = 1/x-7 to find each of the following. (1) (f + g) (-1) (2) (g - f) (x) (3) (fh)(0) (4) (g ○ f) (-

Algebra ->  Functions -> SOLUTION: Use the functions f(x) = 2x +7, g(x) = x squared + 3x, and h(x) = 1/x-7 to find each of the following. (1) (f + g) (-1) (2) (g - f) (x) (3) (fh)(0) (4) (g ○ f) (-      Log On


   

Question 59131: Use the functions f(x) = 2x +7, g(x) = x squared + 3x, and h(x) = 1/x-7 to find each of the following.
(1) (f + g) (-1)
(2) (g - f) (x)
(3) (fh)(0)
(4) (g ○ f) (-1)
(5) (f ○ f) (0)
(6) (g/f) (4)
(7) (g ○ h) (1/2)
(8) (f ○ g ○ h) (8)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I wasn't sure where the fraction ended for your h(x). Let me know if I guessed wrong. Parenthesese help us know what you mean.
Use the functions f%28x%29=2x%2B7, g%28x%29=x%5E2%2B3x, and h%28x%29=1%2F%28x-7%29 to find each of the following.
(1) (f + g) (-1)
%28f%2Bg%29%28x%29=%282x%2B7%29%2B%28x%5E2%2B3x%29
%28f%2Bg%29%28x%29=x%5E2%2B5x%2B7
%28f%2Bg%29%28-1%29=%28-1%29%5E2%2B5%28-1%29%2B7
%28f%2Bg%29%28-1%29=1-5%2B7
highlight%28%28f%2Bg%29%28-1%29=3%29
:
(2) (g - f) (x)
%28g-f%29%28x%29=%28x%5E2%2B3x%29-%282x%2B7%29
%28g-f%29%28x%29=x%5E2%2B3x-2x-7
highlight%28%28g-f%29%28x%29=x%5E2%2Bx-7%29
:
(3) (fh)(0)
%28fh%29%28x%29=%282x%2B7%29%2A%28%281%2F%28x-7%29%29%29
%28fh%29%28x%29=%282x%2B7%29%2F%28x-7%29
%28fh%29%280%29=%282%280%29%2B7%29%2F%280-7%29
%28fh%29%280%29=%280%2B7%29%2F%280-7%29
%28fh%29%280%29=7%2F-7
highlight%28%28fh%29%280%29=-1%29
:
(4) (g o f) (-1)=g(f(-1))
f(-1)=2(-1)+7
f(-1)=-2+7
f(-1)=5
g(f(-1))=g(5)
g(5)=(5)^2+3(5)
g(5)=25+15
g(5)=40
highlight%28%28gof%29%28x%29=40%29
:
(5) (f o f) (0)=f(f(0))
f(0)=2(0)+7
f(0)=0+7
f(0)=7
f(f(0))=f(7)
f(7)=2(7)+7
f(7)=14+7
f(7)=21
highlight%28%28fof%29%280%29=21%29
:
(6) (g/f) (4)
%28g%2Ff%29%28x%29=%28x%5E2%2B3x%29%2F%282x%2B7%29
%28g%2Ff%29%284%29=%28%284%29%5E2%2B3%284%29%29%2F%282%284%29%2B7%29
%28g%2Ff%29%284%29=%2816%2B12%29%2F%288%2B7%29
highlight%28%28g%2Ff%29%284%29=28%2F15%29
:
(7) (g o h) (1/2)=g(h(1/2))
h%281%2F2%29=1%2F%281%2F2-7%29
h%281%2F2%29=1%2F%281%2F2-14%2F2%29
h%281%2F2%29=1%2F%28-13%2F2%29
h%281%2F2%29=-2%2F13
g(h(1/2))=g(-2/13)
g%28-2%2F13%29=%28-2%2F13%29%5E2%2B3%28-2%2F13%29
g%28-2%2F13%29=4%2F169-6%2F13
g%28-2%2F13%29=4%2F169-78%2F169
g%28-2%2F13%29=-74%2F169
highlight%28%28goh%29%281%2F2%29=-74%2F169%29
:
(8) (f o g o h) (8)=(fog)(h(8))
h%288%29=1%2F%288-7%29
h%288%29=1%2F1
h%288%29=1
(fog)(h(8))=(fog)(1)=f(g(1))
g%281%29=%281%29%5E2%2B3%281%29
g%281%29=1%2B3
g%281%29=4
f(g(1))=f(4)
f(4)=2(4)+7
f(4)=8+7
f(4)=15
highlight%28%28fogoh%29%288%29=15%29
:
Happy Calculating!!!