Which of the following represents a function?

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(B) relation $f: A 	o B$ is a function if every element in the domain $A$ has a unique image in the codomain $B$.$1$. For option $A$: $y = \sqrt{x} -

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$y = \sqrt{x} - |x|; \, x \ge 1$

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(B) relation $f: A 	o B$ is a function if every element in the domain $A$ has a unique image in the codomain $B$.$1$. For option $A$: $y = \sqrt{x} - |x|$. If $x $2$. For option $B$: $y = \sqrt{x} - |x|$ with $x \ge 1$. For every $x$ in the domain $[1, \infty)$,there exists a unique real value $y$. Therefore,this represents a function.$3$. For option $C$: $x = y^2$. This implies $y = \pm \sqrt{x}$. For a single value of $x > 0$,there are two values of $y$. Thus,it is not a function.Conclusion: Option $B$ is the correct representation of a function.

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