examstudy
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Is the domain of f(x) the same as the domain for f'(x) in general??
It confuses me because why would they be the same when f-1(x) isn't?

Specifically, I was doing Q4b and got the answers x=-8 and x=2...
I don't know if the -8 is wrong or its something to do with the domain?
QP:http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf
MS:http://pmt.physicsandmathstutor.com/...cimen%20MS%20-
Thank you!

Kevin De Bruyne
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euphrosynay
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in terms of solving the equation, -8 wouldn't be a wrong answer.
it is indeed to do with the domain.

the derivative shows the gradient of a graph at a particular point; you can't find the gradient of a graph at a point that isn't defined.

instead, it's in the small print: f(x) specifies a domain where x > 1. -8 < 1, so any x-value of 1 or below is not defined by this function.

since no point at f(x) is defined at x = -8, you can't differentiate (find a gradient for points in) that part of the graph.

hope this makes sense! everything else was right
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examstudy
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(Original post by euphrosynay)
in terms of solving the equation, -8 wouldn't be a wrong answer.
it is indeed to do with the domain.

the derivative shows the gradient of a graph at a particular point; you can't find the gradient of a graph at a point that isn't defined.

instead, it's in the small print: f(x) specifies a domain where x > 1. -8 < 1, so any x-value of 1 or below is not defined by this function.

since no point at f(x) is defined at x = -8, you can't differentiate (find a gradient for points in) that part of the graph.

hope this makes sense! everything else was right
Ok thank you that does make sense... so I shouldn't think of f'(x) as a separate graph. Think of it as the points with that gradient on f'(x) and seen as x=-8 isn't on f(x)it can't have the gradient and therefore isn't an answer. Where as I should think of f-1(x) (the inverse) as a different graph as the domain is different, but the technical when answering these questions looking at the domain of f(x) will tell me which values of x i should exclude when working out f'(x)??
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euphrosynay
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(Original post by examstudy)
Ok thank you that does make sense... so I shouldn't think of f'(x) as a separate graph. Think of it as the points with that gradient on f'(x) and seen as x=-8 isn't on f(x)it can't have the gradient and therefore isn't an answer. Where as I should think of f-1(x) (the inverse) as a different graph as the domain is different, but the technical when answering these questions looking at the domain of f(x) will tell me which values of x i should exclude when working out f'(x)??
yeah!
the domain of an inverse function f^-1(x) is the range of the function f(x), and vice versa.
and the technical of f(x) is definitely important to know which values to use/exclude for f(x).
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