Math Is Fun Forum

CIV

Member

Registered: 2014-11-09

Posts: 74

Help with an Inverse function please.

I know in general how to find inverse functions but holy hell I can't figure this out. It seems so simple but I can't see the way. I was initially asked to use a graphing calculator graph the function:

Then use the calculators draw inverse feature to draw an inverse relation. Determine whether the inverse relation is an inverse function. Before doing that I decided to just solve for the inverse function algebraically. I learned real quick that I didn't know how. So I used wolfram-alpha and it gave some crazy inverse function that I would of never got as an answer. I wasn't going to ask you guys to help solve that so I got one that has a more simple answer but still can't figure it out.

The thing is is stumbling me is the "+ x". If there was no "+ x" it would be easy to solve.

Also,... I'm wondering, I'm taking Pre-Calc A right now. Should I already know how to do this? Things like this make me feel like I'm behind or not smart enough to do this. But I don't recall my professors ever really going over this. I think. When I see that function I keep thinking to factor.

Last edited by CIV (2015-03-08 05:50:07)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Help with an Inverse function please.

hi CIV,

It's not always easy to construct an inverse as you have discovered here.  But you can learn a lot about a function's (potential) inverse by looking at the graph.  If you reflect a function's curve in the line y = x, you will get the graph of the inverse.

Why?  With the function, you choose an x value and use the formula to work out the corresponding y value.  The inverse is what you get if you start with y and work backwards to get x.  Reflecting does that geometrically.  Here's the two graphs:

As you can see the cubic is 1:1.  That is to say, for every x there is one y and for every y there is one x.  So you know there is an inverse function even if finding a simple expression is impossible.

The quadratic is many:1. That is to say, more than one x gives a particular y value.  So when you start with a y value there is more than one x (except at x = -1/2).  So the inverse is not a function.

To construct a formula for it, you'd have to use the quadratic formula and then you'd get two x values for each y.

Hope that helps

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

CIV

Member

Registered: 2014-11-09

Posts: 74

Re: Help with an Inverse function please.

Thanks Bob. I know all of what you mentioned. Thanks though. I know that if you restrict the quadratic so that all x values are positive, it would then be one to one and an inverse function can be worked out. But for the life of me I can't figure out how to do it. I won't ask my professor because I know he won't do it. Thanks Bob.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Help with an Inverse function please.

Maybe this will work:

Apply the quadratic formula:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob