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MonkeyXu
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#1
Report Thread starter 4 years ago
#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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RDKGames
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#2
Report 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 x=-1 then the function outputs f(-1)=(-1)^2-1=0

But then when x=1 the function outputs f(1)=(1)^2-1=0 also

So your function is not one to one.
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MonkeyXu
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#3
Report Thread starter 4 years ago
#3
(Original post by RDKGames)
If x=-1 then the function outputs f(-1)=(-1)^2-1=0

But then when x=1 the function outputs f(1)=(1)^2-1=0 also

So your function is not one to one.
So x cannot be a negative number when it is in a square from?
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RDKGames
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#4
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#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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MonkeyXu
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#5
Report Thread starter 4 years ago
#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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RDKGames
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#6
Report 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 f(x)=x^2-1, this is a parabola symmetric about x=0 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 x=0, then you can reject EITHER x<0 or x>0 of this function, it doesn't matter which. For simplicity we reject x<0 so our domain is x\geq 0

Since x=-1 is in the rejected domain, it is not defined on the one to one function.

If the domain of our function was x\geq -1, then again, for the region -1 \leq x \leq 1, the function is NOT 1-to-1 because f(-1)=f(1) as an example.
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