SOLUTION: Given the function f(x) = 1/x and g(x) = 1/x-1 , determine the equation for h(x) =f(x)÷ g(x). And state the domain of h(x)

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Question 1205623: Given the function f(x) = 1/x and g(x) = 1/x-1 , determine the equation for h(x) =f(x)÷ g(x). And state the domain of h(x)
Found 3 solutions by josgarithmetic, Edwin McCravy, math_tutor2020:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming you really have f%28x%29=1%2Fx and g%28x%29=1%2F%28x-1%29 then f%2Fg is %281%2Fx%29%28x-1%29. OR %28x-1%29%2Fx.

Domain is all real numbers which are not equal to 0.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Given the function f(x) = 1/x and g(x) = 1/(x-1) , determine the equation for h(x) =f(x)÷ g(x). And state the domain of h(x)

%28f%28x%29%29%2F%28g%28x%29%29=%281%2Fx%29%2F%281%2F%28x-1%29%29

No denominator must be 0

x%3C%3E0, x-1%3C%3E0, 1%2F%28x-1%29%3C%3E0

x%3C%3E0, x%3C%3E1, the 3rd one can never be 0


The domain is:



Edwin

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming that g%28x%29+=+1%2F%28x-1%29 and not g%28x%29+=+1%2Fx+-+1


h(x) = f(x) ÷ g(x)

h(x) = 1%2Fx ÷ 1%2F%28x-1%29

h(x) = 1%2Fx * %28x-1%29%2F1

h(x) = %28x-1%29%2Fx

h(x) = x%2Fx+-+1%2Fx

h(x) = 1+-+1%2Fx
As shown above, there are a few ways we can represent h(x).

We must avoid a division by zero error. To do this, we must kick out x = 0 and x = 1 from the domain.
x = 0 causes f(x) to be undefined
x = 1 causes g(x) to be undefined

Therefore the domain is the set of all real numbers x such that x+%3C%3E+0 and x+%3C%3E+1

The domain in interval notation would be: (-infinity, 0) U (0, 1) U (1, infinity) to represent us poking holes at 0 and 1 on the number line.