Square Root of x
Why does the equation: f(x)=sqrt(x) Not have a curve that goes below the x axis as the the square root of any number has a negative and a positive value? Would this have more implications such as the equation no longer being a function?
(edited 6 years ago)
Original post by Coolconor98
Why does the equation: f(x)=sqrt(x) Not a curve that goes below the x axis as the the square root of any number has a negative and positive value? Would this have more implications such as the equation no longer being a function?
The correct answer is because it's defined that way. The square root function returns the prinicipal square root.
Yeah the reasoning would be that it would no longer be a valid function.
But also just common sense stuff like, if I write down the symbol , there is no ambiguity. Everyone knows that I mean 2.
Otherwise, there would always be ambiguity, do I mean 2, -2, both 2 and -2,
You will soon learn about what is a function and what is not a function.
A function can have one-to-one mapping (think of y=x, every value of x is mapped to its very own value of y) and many-to-one mapping (think of y=x^2, 2 different values of x can map to the same value of y).
It's not a function when it is one-to-many mapping.You're right in thinking that it should go below the x-axis as well but that would make it one-to-many and so no longer a function.
A function can have one-to-one mapping (think of y=x, every value of x is mapped to its very own value of y) and many-to-one mapping (think of y=x^2, 2 different values of x can map to the same value of y).
It's not a function when it is one-to-many mapping.You're right in thinking that it should go below the x-axis as well but that would make it one-to-many and so no longer a function.
(edited 6 years ago)
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