SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM PLEASE: Find the domain of the composite function f o g. f(x) = 2 / x + 10 , g(x) = 60 / x

Question 161482: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM PLEASE:
Find the domain of the composite function f o g.
f(x) = 2 / x + 10 , g(x) = 60 / x
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
f(x) = 2/x + 10
i'll assume that means (2/x) + 10.
hopefully that's right.
if not, resubmit the question.
g(x) = 60/x.
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i assume you are looking for f(g(x)).
if that's what fog means then we're ok.
i'll answer for that.
resubmit the question if i got it wrong.
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g(x) = 60/x (given)
f(x) = (2/x) + 10 (given)
to solve for f(g(x)) you have to replace x with g(x).
this is no different then solving for f(3).
you replace x with 3.
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in this case you replace x with g(x) which means you replace
x with (60/x)
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since f(x) = (2/x) + 10, then

2/(60/x) is the same as (2*x)/60.
you get that by multiplying the numerator and denominator by x.
2*x/(60*x/x) = 2*x/60 since the x in the denominator cancels out.
equation becomes

this becomes

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the domain of f(x) would be all values of x except 0 since you can't divide by 0.
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the domain of g(x) would be the same, i.e. all values of x except 0 for the same reason.
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the domain of f(g(x)), however, would be all values of x since x is now in the numerator rather than the denominator.

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