Does y = sqrt{anything} Qualify as a One-to-One Function?

  • MHB
  • Thread starter mathdad
  • Start date
In summary, the equation "Y = sqrt{anything}" means that Y is equal to the square root of any number or expression within the brackets. To solve this equation, you can use a calculator or find the square root by hand. The value of Y will depend on the number or expression within the square root symbol, and it may have two possible answers. This equation cannot be used to find the square root of negative numbers, as the square root of a negative number is considered an imaginary number. Finally, "Y = sqrt{anything}" is not the same as "Y^2 = anything", as the former is asking for the square root of a number or expression while the latter is asking for the number that, when squared,
  • #1
mathdad
1,283
1
Why must we restrict y = sqrt{anything}?

Is y = sqrt{anything} one-to-one?
 
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  • #2
It depends on the "anything"...for example:

\(\displaystyle f(x)=\sqrt{x}\)

is one-to-one, while:

\(\displaystyle g(x)=\sqrt{\sin(x)+1}\)

is not one-to-one.
 
  • #3
Can you explain the difference between f(x) and g(x)?
 
  • #4
RTCNTC said:
Can you explain the difference between f(x) and g(x)?

Let's plot their graphs to see how they differ. :D

[DESMOS=-0.3404183173408105,19.659581682659205,-0.3390203078626133,6.59940120124406]y=\sqrt{x};y=\sqrt{1+\sin\left(x\right)}[/DESMOS]
 
  • #5
I see they both pass the vertical line test.
 

FAQ: Does y = sqrt{anything} Qualify as a One-to-One Function?

What does "Y = sqrt{anything}" mean?

The equation "Y = sqrt{anything}" means that Y is equal to the square root of any number or expression within the brackets. Essentially, it is asking you to find the number that, when multiplied by itself, equals the given value of Y.

How do you solve "Y = sqrt{anything}"?

To solve "Y = sqrt{anything}", you can use a calculator or follow the steps for finding the square root by hand. First, determine the number or expression within the square root symbol. Then, find the number that, when multiplied by itself, equals the given value of Y.

What is the value of Y in "Y = sqrt{anything}"?

The value of Y in "Y = sqrt{anything}" will depend on the number or expression within the square root symbol. It is important to note that the square root can have two solutions, a positive and a negative, so the value of Y could have two possible answers.

Can you use "Y = sqrt{anything}" to find the square root of negative numbers?

No, "Y = sqrt{anything}" cannot be used to find the square root of negative numbers. The square root of a negative number is considered an imaginary number and cannot be represented by a real number.

Is "Y = sqrt{anything}" the same as "Y^2 = anything"?

No, "Y = sqrt{anything}" and "Y^2 = anything" are not the same. The first equation is asking for the square root of a number or expression while the second equation is asking for the number that, when squared, equals the given value of Y.

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