jamb97
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F(x) = e^x+k, x is a real number and k is a positive constant.

Find f(ln k), simplifying your answer.

I got e^ln k + k

Apparently this is then k+k=2k?

How does e^ln k turn into k?
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joostan
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(Original post by jamb97)
F(x) = e^x+k, x is a real number and k is a positive constant.

Find f(ln k), simplifying your answer.

I got e^ln k + k

Apparently this is then k+k=2k?

How does e^ln k turn into k?
e^{x} and \ln(x) are inverse functions, and f(f^{-1}(x))=x
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jamb97
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(Original post by joostan)
e^{x} and \ln(x) are inverse functions, and f(f^{-1}(x))=x
Sorry but that didn't really help, can you explain a bit more?
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TeeEm
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(Original post by jamb97)
Sorry but that didn't really help, can you explain a bit more?
http://www.thestudentroom.co.uk/show....php?t=3590219
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jamb97
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I think I half understand now. I just find it easier if there's a process with steps to follow.

Say you have F(x)= e^x and F^-1(x)= ln (x).

Then if you do F^-1(F^(x)) then you get ln e^x. From here you can use the power rule to bring x to the front of the term, and then ln (e) cancels to 1 as e^1=e, 1*x = x.

But if you have F(F^-1(x)), you get e^ln(x). I can't see any method/process here other than simply following the rule that inverses applied to each other reverse each other. Is there any method or do you just follow that rule?
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TeeEm
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(Original post by jamb97)
I think I half understand now. I just find it easier if there's a process with steps to follow.

Say you have F(x)= e^x and F^-1(x)= ln (x).

Then if you do F^-1(F^(x)) then you get ln e^x. From here you can use the power rule to bring x to the front of the term, and then ln (e) cancels to 1 as e^1=e, 1*x = x.

But if you have F(F^-1(x)), you get e^ln(x). I can't see any method/process here other than simply following the rule that inverses applied to each other reverse each other. Is there any method or do you just follow that rule?
at this stage it is more important to do rather than to deeply understand.
learn that

ln(ex) = x for all x
elnx = x for all positive x


the explanation is that

F(F-1(x)) = F-1(F()) =x (Identity function)

ex = exp(x)

lnex = ln(exp(x)) =x
elnx =exp(ln(x)) =x
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davros
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(Original post by jamb97)
I think I half understand now. I just find it easier if there's a process with steps to follow.



But if you have F(F^-1(x)), you get e^ln(x). I can't see any method/process here other than simply following the rule that inverses applied to each other reverse each other. Is there any method or do you just follow that rule?
What "rule" are you expecting?

The whole point of inverse functions is that they're defined to reverse the effect of your original function.

So if ln x and e^x are inverse functions of each other, then e^(ln x) = x and ln(e^x) = x. This will work as long as your functions are one-to-one over a particular domain because then it makes sense to talk about finding a unique inverse value.

(As an aside, this is the second question on this I've seen in a couple of days, and I've seen others like it before. Are teachers not teaching this concept properly now??)
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Louisb19
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I like to think about it like this. ln|x| = the power which e is taken to such that it equals to x. e^lnx is the same as saying e to the power of what I just said. e to the power of the number which makes e to the power of it = x will just be x if you follow logic. Sorry that i explained this quite badly, it is hard to phrase in words!
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