SOLUTION: Given the functions f(x)=1/x+6 ; g(x)=x/2-x a.(f ∘ g)(-2) b.(g ∘ f)(-2) c.(f ∘ g)(x) d.(g ∘ f)(x) e.(g ∘ g)(x) f.(g ∘ g)(-2/3) g.(f+g)

Algebra ->  Rational-functions -> SOLUTION: Given the functions f(x)=1/x+6 ; g(x)=x/2-x a.(f ∘ g)(-2) b.(g ∘ f)(-2) c.(f ∘ g)(x) d.(g ∘ f)(x) e.(g ∘ g)(x) f.(g ∘ g)(-2/3) g.(f+g)      Log On


   

Question 780142: Given the functions
f(x)=1/x+6 ; g(x)=x/2-x
a.(f ∘ g)(-2)
b.(g ∘ f)(-2)
c.(f ∘ g)(x)
d.(g ∘ f)(x)
e.(g ∘ g)(x)
f.(g ∘ g)(-2/3)
g.(f+g)(x)
h.(f-g)(x)
i.(f/g)(x)



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given the functions
f(x)=1/(x+6) ; g(x)=x/(2-x)
a.(f ∘ g)(-2) = f[g(-2)] = f[1/2] = 2/13
----------------------------------
b.(g ∘ f)(-2) = g[f(-2)] = g[1/4] = 7/4
----------------------------------
c.(f ∘ g)(x) = f[g(x)] = f[x/(2-x)] = 1/[x/(2-x) + 6] = x/(x+12-6x) = x/(12-5x)
----------------------------------
etc...
Cheers,
Stan H.
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d.(g ∘ f)(x)
e.(g ∘ g)(x)
f.(g ∘ g)(-2/3)