Q. 14.3( 6 Votes )

Find the domain o

Answer :

(i)


Given:


Need to find: Where the functions are defined.


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


Therefore,





It means that the denominator is zero when x = 3 and x = -3


So, the domain of the function is the set of all the real numbers except +3 and -3.


The domain of the function, Df(x) = (- ∞, -3) (-3, 3) (3, ∞).


(ii)


Given:


Need to find: Where the functions are defined.


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


Therefore,






&


It means that the denominator is zero when x = 1 and x = -2


So, the domain of the function is the set of all the real numbers except 1 and -2.


The domain of the function, Df(x) = (- ∞, -2) (-2, 1) (1, ∞).


(iii)


Given:


Need to find: Where the functions are defined.


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


Therefore,






&


It means that the denominator is zero when x = 2 and x = 6


So, the domain of the function is the set of all the real numbers except 2 and 6.


The domain of the function, Df(x) = (- ∞, 2) (2, 6) (6, ∞).


(iv)


Given:


Need to find: Where the functions are defined.


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


Therefore,





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


So, the domain of the function is the set of all the real numbers except -1 and +1.


The domain of the function, Df(x) = (- ∞, -1) (-1, 1) (1, ∞).


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