Expert: Paul Klarreich - 9/8/2009

Question
Hi!

I was wondering if you can explain to me how does one know if a function is defined? My professor keeps saying that we need to see if the fuction is defined to see if it is continuous. Please let me know as soon as you can. Thank you for your time.

Dyanne

Answer
Questioner: Dyanne
Country: United States
Category: Calculus
Private: No
Subject: Survey of Calculus
Question: Hi!

I was wondering if you can explain to me how does one know if a function is defined? My professor keeps saying that we need to see if the fuction is defined to see if it is continuous. Please let me know as soon as you can. Thank you for your time.

Dyanne
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You will not succeed in calculus without paying attention to detail.  Your professor did not say 'the function is defined'; he said 'the function is defined at  x = c'.

Look up the definition of

"A function f(x) is continuous at  x = c."

and you will note that one of the requirements is:

"f(c) exists", which is the same as saying  "f(x) is defined at  x = c"

which means you can compute f(c).  If you cannot, then it is undefined at  x = c.

That's all it means.