Confused about +- symbol use in inverse function

[priceofcarrot]

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

 

[Ray Vickson]

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

 

[AmritpalS]

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

 

[priceofcarrot]

AHHHH! I get it.

This forum rocks, thanks!

 

[AmritpalS]

AHHHH! I get it.

This forum rocks, thanks!

indeed it does

 

[HallsofIvy]

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.

 

[dimension10]

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.

 

[AmritpalS]

For example, if you have $p^2=2$, then $p=\pm2$. Same thing here.

±√2 that is

 

[dimension10]

±√2 that is

Oops, sorry about that. Editted.