SOLUTION: 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

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
RELATED QUESTIONS
find the domain and range of each function. write your answer in interval notation. F(x)= (answered by lwsshak3)

Find the domain and range of the function. (Enter your answers using interval notation.) (answered by stanbon)

Classify the given function as a polynomial function, rational function, or root... (answered by josgarithmetic)

The one-to-one function is defined by f(x) = x/(8-9x) Find f^-1, the inverse of f... (answered by stanbon,Theo)

The one-to-one function is defined by f(x)=6x/(7x-2) . Find f^-1 , the inverse of f... (answered by tommyt3rd)

The one-to-one function f is defined below. =f(x)=x/5x-4 Find f^-1, where f^-1 is the... (answered by greenestamps)

Find the range of the function and write it using interval notation:... (answered by jim_thompson5910,lwsshak3)

f(x)=2x+4 find the inverse function, domain and range of inverse function (answered by stanbon)