Does the input-output relation definition hold for radical functions?

Asked Jul 12 '23 at 14:35

Active Jul 12 '23 at 14:35

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For example, I have a function, $f\left(x\right)=\sqrt{x}$ where, x >= 0. For an input of x = 4 for example, the square root would be ±2.

Does that not mean there are two answers/outputs, 2 and -2?

But the definition of a function states that every input has exactly one output.

Please tell me what I am missing here. Thanks.

asked Jul 12 '23 at 14:35

zayeedBS

1

Does this answer your question? Is sqrt(x) a function? Does it matter if a domain is given? – aqualubix Jul 12 '23 at 14:44
You defined the function to be $f(x)=\sqrt x$, not $f(x)=-\sqrt x$ or some other thing. – Paul Jul 12 '23 at 15:43
For positive real $x$, the symbol $\sqrt{x}$ always represents the positive square root. – eyeballfrog Jul 12 '23 at 16:21

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