Confused about +- symbol use in inverse function

In summary, the ± symbol is necessary in the equation y = ± sqrt(x+4) because there are two values for y that will satisfy the equation and if x = 0, y could be +2 or -2. This is because when taking the square root, both positive and negative values could result in the same number when squared. This also shows that the original function does not have an inverse.
  • #1
priceofcarrot
32
0


Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given.


You have :

y = x^2 - 4
x = y^2 - 4
y^2 = x + 4
y = ± sqrt(x+4)


I don't get why there is a ± symbol there. My book says that it's necessary because there are two values for y that will satisfy the equation, and that if x = 0, y could be +2 or -2.


I understand that y could = +2, because sqrt 4 = +2, but I don't see how it could equal -2.

How would I know that I should include the ± symbol in front of the sqrt(x+4)? Thanks
 
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  • #2
priceofcarrot said:
Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given.


You have :

y = x^2 - 4
x = y^2 - 4
y^2 = x + 4
y = ± sqrt(x+4)


I don't get why there is a ± symbol there. My book says that it's necessary because there are two values for y that will satisfy the equation, and that if x = 0, y could be +2 or -2.


I understand that y could = +2, because sqrt 4 = +2, but I don't see how it could equal -2.

How would I know that I should include the ± symbol in front of the sqrt(x+4)? Thanks

What is (-2)*(-2)?

RGV
 
  • #3
Whenever you take the square root of something it requires a +or- because the square of either the negative or positive value of that term would yield the same number when it is squared. for instance (-x)^2=(x)^2

since you are squaring y, you must be aware that the sqrt of (x+4) will net y regardless if it is positive or negative
 
  • #4
AHHHH! I get it.

This forum rocks, thanks!
 
  • #5
priceofcarrot said:
AHHHH! I get it.

This forum rocks, thanks!

indeed it does
 
  • #6
Note, by the way, that what this is saying is that the original function does NOT HAVE an inverse! A function has an inverse if and only if it is "one to one". That is, there is only one value of x that gives a specific y value. It that is not true, we can choose a specific one of the x values for a given y value, as here choosing "+" or "-", which is equivalent to choosing a subset of the original function.
 
  • #7
priceofcarrot said:

Homework Statement


Homework Equations


The Attempt at a Solution



Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given.You have :

y = x^2 - 4
x = y^2 - 4
y^2 = x + 4
y = ± sqrt(x+4)I don't get why there is a ± symbol there. My book says that it's necessary because there are two values for y that will satisfy the equation, and that if x = 0, y could be +2 or -2. I understand that y could = +2, because sqrt 4 = +2, but I don't see how it could equal -2.

How would I know that I should include the ± symbol in front of the sqrt(x+4)? Thanks

For example, if you have ##p^2=2##, then ##p=\pm\sqrt2##. Same thing here.
 
Last edited:
  • #8
dimension10 said:
For example, if you have ##p^2=2##, then ##p=\pm2##. Same thing here.

±√2 that is
 
  • #9
AmritpalS said:
±√2 that is
Oops, sorry about that. Editted.
 

1. What does the +- symbol in an inverse function represent?

The +- symbol in an inverse function represents the two possible solutions to an equation. It indicates that the inverse function has both a positive and negative solution.

2. How do I know when to use the +- symbol in an inverse function?

The +- symbol is typically used when solving equations that involve square roots or absolute values. It is used to account for both the positive and negative solutions to the equation.

3. Can the +- symbol be used in other types of functions?

No, the +- symbol is only used in inverse functions. It is not commonly used in other types of functions.

4. Is there a specific order in which the +- symbol should be used in an inverse function?

No, there is no specific order in which the +- symbol should be used. It is usually placed in front of the square root or absolute value symbol, but this can vary depending on the equation.

5. Are there any tips for simplifying equations with the +- symbol in inverse functions?

One tip is to always check your solutions by plugging them back into the original equation. Another tip is to combine like terms before using the inverse function to simplify the equation.

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