Math Is Fun Forum

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Need help with inverse functions

Working with Stewart's "Calculus, Early Transcendentals"
Stuck on two problems:

1.6 #17
If

, find

.

The answer here is almost obvious:

.
Just by simple brute force approach (plug various numbers into x and once g(x) become 4, the value of x is the value of

But I do not think that is the approach expected from students...
Unfortunately I do not see how to make an inverse function. Where to start?

1.6 #26
Find inverse of the function:

Same problem here. Where to start? How to take

outside?

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Need help with inverse functions

The second one is easy enough.

It should be simple enough to solve for x from there.

The first question is a bit trickier, I don't know offhand of a good way of finding the inverse function to that.

Edit: After searching around it seems that the first problem does not have a simple inverse function.  Your only options there are trial and error or some method of numerical approximation.

Last edited by TheDude (2012-06-11 07:33:02)

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Wrap it in bacon

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Need help with inverse functions

Thank you.
I got the second one.

As for the first... Well I thought of using the numerical approximation as a justification for finding

without formally finding the

itself.
Unfortunately, (or luckily) in that case we do not need approximation. The x=0 already gives the y=4. Not much of approximation...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Need help with inverse functions

hi White_Owl

And that will be the only solution.

Both x and e^x are increasing functions so once the curve crosses y = 4 for the first time, it won't do it again.  (see graph below)

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Need help with inverse functions

But he doesn't want to guess. He wants to somehow get the value 0.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Need help with inverse functions

hi Stefy,

Well that might be what White_Owl would like, but it isn't what the question asks for.

It says find inv g (4).

Now g is an increasing and continuous function so it has a unique inverse for all reals.

So once you have a value (and spotting it is easy) all you have to do is prove that it fits (ie. show g(0) = 4 ) and the question is legitimately complete.

By all means find an analytic way of getting this if you must ... publish when you have and we'll add your name to Agnishom's list.

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