Q. 34.8( 5 Votes )

Find the domain and the range of each of the following real function:

Answer :

Given:


Need to find: Where the functions are defined.


Let, ---- (1)


To find the domain of the function f(x) we need to equate the denominator of the function to 0.


Therefore,


x – 5 = 0


x = 5


It means that the denominator is zero when x = 5


So, the domain of the function is the set of all the real numbers except 5.


The domain of the function, Df(x) = (- ∞, 5) (5, ∞).


Now, to find the range of the function we need to interchange x and y in the equation no. (1)


So the equation becomes,





To find the range of the function f(x1) we need to equate the denominator of the function to 0.


Therefore,


x = 0


It means that the denominator is zero when x = 0


So, the range of the function is the set of all the real numbers except 0.


The range of the function, Rf(x) = (- ∞, 0) (0, ∞).


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