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what is the basis of equating the 2 square roots ?

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- #1

- 51

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what is the basis of equating the 2 square roots ?

- #2

Simon Bridge

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Can you think of another way to show it is 1-1?

- #3

Mark44

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What is the definition of a function being one-to-one?if

View attachment 94299 then to prove an inverse of this exists the following has been done to show that it is one to one

View attachment 94298

what is the basis of equating the 2 square roots ?

- #4

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an output can have only one input ,but what i don't understand is the basis of the expressionWhat is the definition of a function being one-to-one?

- #5

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yes i can reach the conclusion if we draw a graph but i'm confused about how to arrive at the conclusion (one to one ) using this dataCan you think of another way to show it is 1-1?

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jbriggs444

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If you graph it, can you think of a specific feature of the graph that you could phrase mathematically?yes i can reach the conclusion if we draw a graph but i'm confused about how to arrive at the conclusion (one to one ) using this data

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HallsofIvy

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That is exactly what you said above: "an output can have only one input". If x and y are the "inputs" for the "outputs", f(x) and f(y), and they are the same, f(x)= f(y), so they are the same output, the inputs must be the same: x= y. Showing that "if f(x)= f(y) then x= y" is exactly the same as showing "an output can have only one input".an output can have only one input ,but what i don't understand is the basis of the expressionView attachment 94307

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FactChecker

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It is the "If" part of an "if-then" statement. It is not proven, it is assumed. So there is no need for a "basis" for the statement.an output can have only one input ,but what i don't understand is the basis of the expressionView attachment 94307

This is all that you need to prove to show that the function has an inverse.

- #9

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That is exactly what you said above: "an output can have only one input". If x and y are the "inputs" for the "outputs", f(x) and f(y), and they are the same, f(x)= f(y), so they are the same output, the inputs must be the same: x= y. Showing that "if f(x)= f(y) then x= y" is exactly the same as showing "an output can have only one input".

It is the "If" part of an "if-then" statement. It is not proven, it is assumed. So there is no need for a "basis" for the statement.

If(x/(x+1))^{0.5}= (y/(y+1))^{0.5}

thenx=y.

This is all that you need to prove to show that the function has an inverse.

so why have you proved an input equals an input ? when what we should prove is that for two particular inputs the OUTPUT will be the same only if those two inputs are equal.

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FactChecker

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