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Find the domain and the range of each of the following real function:
Need to find: Where the functions are defined.
To find the domain of the function f(x) we need to equate the denominator of the function to 0.
x – 3 = 0
⇒ x = 3
It means that the denominator is zero when x = 3
So, the domain of the function is the set of all the real numbers except 3.
The domain of the function, Df(x) = (- ∞, 3) ∪ (3, ∞).
Now if we put any value of x from the domain set the output value will be either (-ve) or (+ve), but the value will never be 6
So, the range of the function is the set of all the real numbers except 6.
The range of the function, Rf(x) = (-∞, 6) ∪(6, ∞).