Math Help Range
January 22nd, 2011
Question: Math Help, domain and range.. all real numbers??? CONFUSED.. PLEASE HELP!!!?
in math we are doing functions/function notation and i was just wondering how do you know when to put “all real numbers” for domain and range??
please help, this is urgent!!!!!
Answer: Do it wherever it makes sense. For example:
f(x) = x + 1
has a (largest possible) domain of all real numbers, since you can plug any value of x in and get a valid result for f(x). It’s range will also be all real numbers, since you can get every real number by plugging a value in for x. Another example:
g(x) = 1 / sqrt(x – 1)
This does not have a domain of all real numbers. Think about x = 0. That would leave a square root of a negative number. Think about x = 1. The square root of 0 is valid, but it would leave a division by 0. This function has a (largest possible) domain of x > 1, since every value of x > 1 can be plugged in, and you’ll get a real number back.
As for the range, you know that g(x) > 0 for all x, since sqrt() of anything will return a positive value. Other than that, the range will be all other numbers (this is a little bit more difficult to prove).
Things to look for:
- division by 0 is never defined
- square roots, fourth roots, sixth roots, etc take and return non-negative (i.e. x>=0)
- any logarithms take strictly positive values (i.e. x > 0)
Math Functions & Techniques : How to Find the Domain & Range of a Function
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