Question

Find the domain and the range of the real function f defined by f (x) = |x – 1|.​

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

Find the domain and the range of the real function f defined by f (x) = |x – 1|.

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️Given real function,

➡️f (x) = |x – 1|

➡️Clearly, the function |x – 1| is defined for all real numbers.

➡️Hence,

➡️Domain of f = R

➡️Also, for x ∈ R, |x – 1| assumes all real numbers.

➡️Therefore, the range of f is the set of all non-negative real numbers.

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Answer 2

Here value of domain (x) can be any real number

Hence domain = R(All real numbers)

We note that range f(x)= 0 or positive numbers.So ,range cannot be negative.

Hence range= non negative numbers