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Question 192313: Find the domain and range (write in interval notation) of the given function using knowledge about the inverse function. f(x)=2x+1/3x-5
Answer by abraham(1)   (Show Source):
You can put this solution on YOUR website! Clearly,The function is not defined at the pre image 3x-5=0 i.e x=5/3, because the remainder is zero at this value and the value of the function become meaningless. If X does not equal 5/3 then the function is defined in the whole of Real numbers.Therefore the domain is R-{5/3}
Let y=2x+1/3x-5
then 3xy-5y=2x+1,
then x(3y-2)=5y+1,
then x=5y+1/3y-2
From this relation it is clear that x is not defined when y=2/3 (i.e 3y-2=0) Therefore the Range of the function is R-{2/3}
Notation:R is the set of all real numbers and R-{2/3} is the set of all real numbers excluding 2/3
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