# Restricted domain

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#1
f(x) = x^2 minus 1 is not a one one function. Restrict the domain such that it is a one one function and the range is not affected.
This was the question and the answer was x must be more than or equals to 0. However, I think x can also be minus 1. Please help.
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4 years ago
#2
(Original post by MonkeyXu)
f(x) = x^2 minus 1 is not a one one function. Restrict the domain such that it is a one one function and the range is not affected.
This was the question and the answer was x must be more than or equals to 0. However, I think x can also be minus 1. Please help.
If then the function outputs

But then when the function outputs also

So your function is not one to one.
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#3
(Original post by RDKGames)
If then the function outputs

But then when the function outputs also

So your function is not one to one.
So x cannot be a negative number when it is in a square from?
0
4 years ago
#4
(Original post by MonkeyXu)
So x cannot be a negative number when it is in a square from?
What do you mean??

A negative number squared gives a positive number.
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#5
(Original post by RDKGames)
What do you mean??

A negative number squared gives a positive number.
However, you rejected -1 because it is not a one one function. So is it whenever there is a x^2, x must be a positive number? Because every value of y can only have one value of x. (That was a fast reply though)
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4 years ago
#6
(Original post by MonkeyXu)
However, you rejected -1 because it is not a one one function. So is it whenever there is a x^2, x must be a positive number? Because every value of y can only have one value of x. (That was a fast reply though)
A one to one function is a function which has one input and one output accordingly.

Take , this is a parabola symmetric about and has a U shape.

Clearly, on the natural domain of this function, you get a single output for 2 different inputs. As this function is symmetric about , then you can reject EITHER or of this function, it doesn't matter which. For simplicity we reject so our domain is

Since is in the rejected domain, it is not defined on the one to one function.

If the domain of our function was , then again, for the region , the function is NOT 1-to-1 because as an example.
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