Function inverses example 2 | Functions and their graphs | Algebra II | Khan Academy

Function Inverses Example 2

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[iwuvvparamore]

Just in case you're wondering,
a root is when the graphed line meets or intercepts
the x-axis :)

[Daski]

one perhaps dumb question but I'd like to ask if the inverse of a function really is changing the dependent variable to the independent

I mean if you have say
y = 2x + 1
x = 1/2y - 1/2
if you graph the f(x) you get the same as if you graph the f(y), it is only when you change the y to x and x to y in the second function (the inverse) that you get the correct graph.

Does it only become the inverse function when the switching of the y and x is done? I mean if you solve for x with respect to y you will still obviously get the same graph.

Thanks!

[alieminemgmailcom]

Can't u just expand (x+2)^2 using the identity (a+b)^2?
Please answer soon!

[KillraStealer]

the problem is that 2 different x gives you the same y. so the one y need to give you 2 different x if you don't constrain it.

[Karnex]

Sorry if stupid question, but how he does that blue line y=x? It is different in every video

[bigstuff]

Thanks for clearing up the re-naming thing.

[iwuvvparamore]

It's an application question.
When you are told to graph a value of "possible real roots"
Then you use the ≥ sign because the roots can be real in situations
Where x is either > 0 or = to zero.
Conversely, if the question asks you to find the value of x when there are "no possible roots", then you use x < 0 & to find 1 real root the function is x = 0.
Conclusively,
1)When the number of REAL roots is not specified : x ≥ 0
2) When roots are NOT real : x < 0
3) When there is only one root : x = 0

[mtdeezy]

I graphed the inverse of f(x) = (x+2)^2 + 1 with no constraint and it worked just fine.

[goshiluvarchie]

Someone please help? How did he find the constraint on x for the inverse function? (x >= 1)

[HaiderRehman]

please anyone explain the relation of slope with inverse function

[iwuvvparamore]

So in this case,
the value of x is : x < 0

Why ?

Because the graph does not touch the x-axis.
It does touch the y-axis, but NOT the x-axis
Therefore, it has No real roots and x is -2 .
^ Notice how the value of x ( -2 )
corresponds to the "no real roots" rule ( x < 0 )

[iwuvvparamore]

Hope this helped :D
Oh and don't worry, this isn't that complicated.
I'm just a Year 12 student as well hahaha

[AdmatHakodesh]

"for y is greater than or equal to 1"