# Thread: Multiple solutions for limit of an inverse function without a calculator

1. ## Multiple solutions for limit of an inverse function without a calculator

I was just merrily some maths, when I came up with this problem.

I don't know LATEX or any of that fancy stuff, so I'll just put it in paint.

To solve it, instead of finding the inverse function, just plug in -3 to the equation as g(x), and you get the solution, which is pi.

Well, this is all and well, right?
HOWEVER, Wolfram Alpha and my handy dandy TI-89 disagree.
Plugging the equation into Wolfram Alpha, I get not 1 point, pi, but also 3 other random points which seemingly are not supposed to exist but still do.
2-x&#43;5cosx&#43;pi&#43;3&#61;0 - Wolfram|Alpha
This is a problem, since the problem was specifically supposed to be solved without a calculator.

How would one achieve such calculations without the aid of a calculator?

2. Originally Posted by Yangliu239
I was just merrily some maths, when I came up with this problem.

I don't know LATEX or any of that fancy stuff, so I'll just put it in paint.

To solve it, instead of finding the inverse function, just plug in -3 to the equation as g(x), and you get the solution, which is pi.

Well, this is all and well, right?
HOWEVER, Wolfram Alpha and my handy dandy TI-89 disagree.
Plugging the equation into Wolfram Alpha, I get not 1 point, pi, but also 3 other random points which seemingly are not supposed to exist but still do.
2-x&#43;5cosx&#43;pi&#43;3&#61;0 - Wolfram|Alpha
This is a problem, since the problem was specifically supposed to be solved without a calculator.

How would one achieve such calculations without the aid of a calculator?
g(x) is a many-to-1 function therefore the inverse is a 1-to-many relation. Therefore the given limit does not exist unless the domain of g(x) is restricted. Since pi is the only solution that can be found without a calculator, it's a fair bet that the domain has been restricted so that only that solution exists. I suggest you go back and look at the exact wording of the question.

3. Originally Posted by Yangliu239
I was just merrily some maths, when I came up with this problem.

I don't know LATEX or any of that fancy stuff, so I'll just put it in paint.

To solve it, instead of finding the inverse function, just plug in -3 to the equation as g(x), and you get the solution, which is pi.

Well, this is all and well, right?
HOWEVER, Wolfram Alpha and my handy dandy TI-89 disagree.
Plugging the equation into Wolfram Alpha, I get not 1 point, pi, but also 3 other random points which seemingly are not supposed to exist but still do.
2-x&#43;5cosx&#43;pi&#43;3&#61;0 - Wolfram|Alpha
This is a problem, since the problem was specifically supposed to be solved without a calculator.

How would one achieve such calculations without the aid of a calculator?
What you typed into Wolfram Alpha is not the same as what you have in the png file.

Also the definition of g(x) in the png needs further simplification or the insertion of brackets.

CB