If I say x^2=4, x can be 2 or - 2. So why If I say y=x^1/2 and if x can be 4, why can't y be 2 or - 2?The yellow line is irrelevant because it is the curve describing [imath]y = - \sqrt{x}.[/imath] Remember that the square root function is defined to be non-negative.
y2 = x → y = √x ................ only positive values by definition.If I say x^2=4, x can be 2 or - 2. So why If I say y=x^1/2 and if x can be 4, why can't y be 2 or - 2?
So why If I say y=x^1/2 and . . .
so if f(x)=sqrt(4) f(x)=2?The WHOLE POINT of a function is that it never gives an ambiguous answer. It is never one-to-many.
So it is absolutely true that
[math](-4)^2 = 16 = (4)^2 .[/math]
But when we define the square root as a FUNCTION, we have to choose which of those we mean. So, one definition of the square root function is
[math]f(x) = \sqrt{x^2} \iff f(x) = |x|[/math]
Yes though I would prefer to sayso if f(x)=sqrt(4) f(x)=2?