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This is probably similar to a question I recently asked, but I can't quite make he connection.
Question:
Given that the domain of g is, find the least value of a such that g has an inverse function.
Drawing a graph of the function, I notice that the first positive maximum is, which incidentally also happens to be the answer to the question. Why is this?
Thank you in advance.
there can only be an inverse if each x value corresponds to a single y value.
Your graph has a turning point a. starting from x=0:
as you increase x, y increases
after
Can you see that this means there must be some y values that occur twice, once to the right of
it might be clearer on this graph:
y=3x/(5+x^2) from -10,10 - Wolfram|Alpha
Use the [tex]...[/tex] tagsQuote:
Originally Posted by mtpastille
This is probably similar to a question I recently asked, but I can't quite make he connection.
Question:
[Latex is misbehaving: g(x)=3x/(5+x^2)]
So that [TEX]g(x) = \frac{3x}{5+x^2}[/TEX]
becomes
Oh, so it's that simple! The horizontal line test springs to mind, that's what I'd forgotten. Thank you :)
Just found this when searching for an explanation to this problem that was driving me crazy.
My problem now is that when you compute the inverse we have.
This is confirmed in the markscheme.
Therefore whenthe inverse is complex. I confirmed this by graphing the answer to part c from the markscheme on my TI84. It doesn't graph as it's graphed in the markscheme. As x approaches zero from the right g-1(x) approaches zero as well, not infinity.
Am I missing something here?