how do I find the inverse of f(x)=(x-2)^2+4?

Question

anonymous · Answer

You know that f(x) is the same as y so you can rewrite the equation as$$y=(x-2)^2+4$$ Now all you have to do is interchange the x and y and solve so simplify and solve this for y$$x=(y-2)^2+4$$

anonymous · Answer

ok I get that thank you

anonymous · Answer

so it would be square root ofx-4 +2 right?

hartnn · Answer

if you meant $\sqrt{x-4}+2$
then its correct.

anonymous · Answer

so how come when I put them in the calculator to graph them they arent opposite of each other

hartnn · Answer

opposite ? in what sense ?
also more accurate answer will be $\pm \sqrt{x-4}+2$

anonymous · Answer

they are supposed to be the same thing but going in different directions on the graph

hartnn · Answer

no, who told you that ?

hartnn · Answer

like ln x and e^x are inverse of each other but they don't go in opposite direction....

anonymous · Answer

|dw:1362657878171:dw|
thats a sketch of the first equation isnt the second supposed to be the same thing but going down

hartnn · Answer

no! you can't just visualize an inverse function, you have to get it algebraically...

anonymous · Answer

well in my assignment I am supposed to graph it

hartnn · Answer

you are talking about mirror image with x axis as mirror, thats not what inverses are...

hartnn · Answer

so, just graph the functions individually.... anything asked to verify ?

anonymous · Answer

Hi,  I'm Dr. Professor
to find inverse you have to follow these steps:

Lets first start with an example,
We have , f(x) = 2x+3

|dw:1362657923585:dw|

Right, May be this much is clear.

Now the Inverse function goes in this way,

|dw:1362658040262:dw|

So ,  the inverse of:   2x+3   is:   (y-3)/2