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### A Function of a Function

```
Date: 6/19/96 at 14:51:12
From: Scott Turner
Subject: A Function of a Function

You answered my last question so quickly.  I am so impressed.  Thanks
so much for the help.  Here is another one.  I understand the concept
but I don't know how to put it into words:

Suppose that f(x) is O(g(x)). Does it follow that 2 to the power f(x)
is O(2 to the power g(x))?

Again, thanks for your invaluable service.

ST
```

```
Date: 6/20/96 at 13:51:3
From: Doctor Tom
Subject: Re: A Function of a Function

Nope.

Let f(x) = 2x and g(x) = x.  f = O(g) since for large x,
f(x) < 2.1*g(x).  But there's no constant M such that
2^(2x) < M*2^x.  If so, M must be greater than 2^x, for
all x, which is clearly impossible.

-Doctor Tom,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

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