A functions has the most restricted domain is C. [tex]y=\sqrt{x}[/tex]
What is function?
"A function is an expression that takes an input and produces only one possible output for that given input."
What is domain of a function?
"A domain of a function is the set of possible input values for which function is well-defined."
What is restricted domain of a function?
"Some functions are not defined for all the real numbers, and thus are evaluated over a restricted domain."
For given situation,
Consider function [tex]A.[/tex] [tex]y=\frac{1}{x}[/tex]
The domain above function is all real numbers except [tex]x=0[/tex], as function is not defined for [tex]x=0[/tex]
So, the domain of [tex]y=\frac{1}{x}[/tex] is [tex]R-[/tex] {[tex]0[/tex]}.
Consider function [tex]B.[/tex] [tex]y=x^{2}[/tex],
The domain of this function is the set all real numbers as, function is well defined for all real values.
That is, domain of [tex]y=x^{2}[/tex] is [tex]R[/tex] .
Consider function [tex]C.[/tex] [tex]y=\sqrt{x}[/tex]
The domain of this function all non-negative real numbers, as square-root of negative real number cannot be determined.
So, the domain of function [tex]y=\sqrt{x}[/tex] is [tex]R^{+}[/tex] ∪ {[tex]0[/tex]}.
Consider function [tex]D.[/tex] [tex]y=|x|[/tex]
The domain of this function set of real numbers. [tex]R[/tex]
Hence, the parent function having most restricted domain is [tex]y=\sqrt{x}[/tex].
Therefore, the correct answer is option C.
Learn more about domain of function here,
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