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#1 2009-10-07 13:43:25
- MathsIsFun
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Operations with Functions
Please have a look at Operations with Functions and tell me anything wrong or lacking, thanks.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#2 2009-10-07 23:48:40
- mathsyperson
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Re: Operations with Functions
Looks mostly good, but in your 'But Not Always' section you've got an (x-1)² where there should be an (x-3)², and there's an 'ex' that looks like a typo.
I'd also say that if f(x) = (x-3)²/(x-3) then f(3) is undefined, and we can't just simplify the function to make it x-3. There would be a limit at that point, but not a value.
Why did the vector cross the road?
It wanted to be normal.
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#3 2009-10-08 09:49:26
- MathsIsFun
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Re: Operations with Functions
Thank you.
You are right about the "But Not Always" example ... if I can't think of a correct example I will abandon that section.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#4 2009-10-08 10:23:45
- MathsIsFun
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Re: Operations with Functions
How about f(x) = x + 1/x and g(x) = x
(fg)(x) = x²+1
???
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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#5 2009-10-08 11:16:10
- bobbym
- bumpkin
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- Registered: 2009-04-12
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Re: Operations with Functions
Hi MathsisFun;
Some functions have a removable singularity.
Def: When the function is bounded in a neighbourhood around a singularity, the function can be redefined at the point to remove it; hence it is known as a removable singularity. In contrast, whe a function tends to infinity as z approaches 0; thus, it is not bounded and the singularity is not removable,
According to this and I found other sites that agree. Just google for removable singularity.
f(x) = sin(x) / x , f(0) is defined and is equal to 1 This is the example they all give for a removable singularity.
Last edited by bobbym (2009-10-08 11:17:40)
In mathematics, you don't understand things. You just get used to them.
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