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Question

Find the domain and the range of the real function f defined by f(x)=(x1)

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Solution

The given real function is f(x)=x1
It can be seen that x1 is defined for (x1)0
i.e., f(x)=(x1) is defined for x1
Therefore the domain of f is the set of all real numbers greater than or equal to 1 i.e.,
the domain of f =[1,)

As x1
(x1)0
x10
f(x)0
Therefore the range of f is the set of all real numbers greater than or equal to 0
i.e., the range of f =[0,)

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