SOLUTION: For {{{f(x) = 2/(x-3)}}} , solve for the domain and range in interval notation
I found already the domain:
(-infinity,3) u (3,+infinity)
and i'm confident that it is correct
Algebra.Com
Question 1041914: For , solve for the domain and range in interval notation
I found already the domain:
(-infinity,3) u (3,+infinity)
and i'm confident that it is correct.
What confuses me is finding the Range.
I'm not confident on my answer:
(- infinity , 2] u [2, + infinity)
for the + infinity there, i mean it to be positive but approaching zero making 2 as the maximum output that can be obtained in this function.
I'm lost in that part. so can you give me the correct range in INTERVAL NOTATION and explain it efficiently? thanks.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's find the inverse of the function.
Replace f(x) with y
Swap x and y. Now solve for y.
Multiply both sides by y-3
Distribute
Add 3x to both sides
Divide both sides by x
so is the inverse of
As a side project, I recommend you confirm that and . I'll leave this for you to do on your own.
--------------------------------------------
Why is the inverse so important? Because the domain of the inverse function is the same as the range of the original function. Recall that the domain and range swap when it comes to inverses and their original counter-part functions. The swap occurs because x and y are swapped.
The domain of g(x) is any number but x = 0 to avoid division by zero errors.
So the range of f(x) is the same thing, just with a different variable: y will be any number but y = 0.
The range of f(x) in interval notation is (-infinty, 0) U (0, infinity)
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