SOLUTION: indicate the domain: a(x)=(x+2)^-1

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Question 386072: indicate the domain: a(x)=(x+2)^-1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
When finding domains, you need to ensure that no numbers in the domain will make
  • a denominator zero
  • a radicand (expression within a radical) of an even-numbered root negative
  • a base or argument to a logarithm zero or negative
  • other "illegal" expressions (for example, tan%28pi%2F2%29)

Your function has no radicals or logarithms. And it may appear that it does not have a denominator. But if you understand what -1 as an exponent means then you will realize that we really do have a denominator:
a%28x%29+=+%28x%2B2%29%5E%28-1%29+=+1%2F%28x%2B2%29
So we have to make sure that the domain includes only numbers that make the denominator something other than zero. The way to determine this is to figure out what number(s) make the denominator zero and then exclude them from the domain. So we set the denominator equal to zero and solve:
x + 2 = 0
Subtract 2 from each side and we get:
x = -2
This is the only number that makes the denominator zero. So this is the only number we must exclude from the domain. So the domain is all real numbers except -2.