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(39616) (Show Source): You can put this solution on YOUR website! Assuming you really have and then is . OR .
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)
No denominator must be 0
, , , , the 3rd one can never be 0
The domain is:
Edwin
h(x) =
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 and
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.