Q. 45.0( 4 Votes )

Find the domain a

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,


2 – x = 0


x = 2


It means that the denominator is zero when x = 2


So, the domain of the function is the set of all the real numbers except 2.


The domain of the function, Df(x) = (- ∞, 2) (2, ∞).


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(x) we need to equate the denominator of the function to 0.


Therefore,


x + 1 = 0


x = -1


It means that the denominator is zero when x = -1


So, the range of the function is the set of all the real numbers except -1.


The range of the function, Rf(x) = (- ∞, -1) (-1, ∞).


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