Find the inverse of this function f(x)=2-sqrt(x/2+3)
State domain and range of the function and the inverse :)

Question

Find the inverse of this function f(x)=2-sqrt(x/2+3)
State domain and range of the function and the inverse :)

thomas5267 · Answer

Rearrange $y=2-\sqrt{\frac{x}{2}+3}$ so that x is on one side and y is on another.

anonymous · Answer

ok I get y = 2x^2-8x+1

e.mccormick · Answer

Did you forget to multiply through the +1 with the 2?

Also, do you know how to find the domain and range?

anonymous · Answer

oops yes I did :(

anonymous · Answer

for f(x) I have the domain to be >or =to -6 and the range to be y< or = to 2

e.mccormick · Answer

Yes.  Basically, you find a valid domain and then see what that would result in as a valid range.

anonymous · Answer

i have a parobola for the inverse so I will have to restrict?

e.mccormick · Answer

Well, if it is a one to one inverse, the domain and range will actually reverse.

e.mccormick · Answer

But a parabola has a domain of $(-\infty,\infty)$, so...

anonymous · Answer

ah so swapping the domains I am restricting anyway?

e.mccormick · Answer

Yes, when you make the range of the funtion into the domain of the inverse, you automatically restrict the inverse.  This causes the range of the inverse match the domain of the function.

anonymous · Answer

ahhhhh so what I have is right then? i.e. the inverse equation and the domain and range, so for inverse x$$x \le2    $$ $$y \ge-6$$

e.mccormick · Answer

Yep.  Oh, and if you use `$` and `$`you can do the $\LaTeX$ inline rather than a seperate block:

To get:
$f^{-1}(x)$ has a domain of $x\le 2$ and a range of $y\ge -6$.
I type:
```
$f^{-1}(x)$ has a domain of $x\le 2$ and a range of $y\ge -6$.
```

anonymous · Answer

oh wow thank you :)

anonymous · Answer

what about the inverse of $g(x) = 2/(3-x)+2$

e.mccormick · Answer

Lots of $\LaTeX$ tutorials here: http://openstudytutorials.weebly.com/tutorials-by-topic.html#computer In my "Introduction to Mathjax-LaTeX with videos" I go over how to type it in or use editors. In a few other the other ones they go into a lot more of the art use, but I wanted to make sure someone covered the absolute basics.

thomas5267 · Answer

Wikibooks also have a LaTeX tutorial.  It contains a nice section of Mathematics and Advanced Mathematics use.

thomas5267 · Answer

A good way to learn mathematical LaTeX is go to the Wikipedia page of the mathematics you need to typeset and see the source.  ProofWiki, AoPSWiki or other mathematical Wikis should work too.

e.mccormick · Answer

With fractions, watch out for your undefined area where the divisor is 0.

anonymous · Answer

So I have asymptotes in the original function of x=3 and y=2, where x is an element of all the reals except 3 and y an element of all the reals except 2

e.mccormick · Answer

Yah. Which looks like this: https://www.desmos.com/calculator/4e3qq0pdcn