



 
Hi Camille, There is no general procedure for finding the domain or range of a function. You should read what Chris wrote in response to a similar question. The example you give shows one kind of trap you can fall into. Find inverse: y = 3 / sqrt (x2)
This function has a domain of all x except x = 0 so is that the range of the original function? Look at the original function, y = 3 / sqrt (x2). You can see that y can't be negative. Thus for example 1 is in the domain of y = ^{9}/_{x2} + 2 but it's not in the range of y = 3 / sqrt (x2). What did I do wrong? The trap I fell into is in squaring x = 3 / sqrt (y  2). In this expression x must be positive and when I squared both sides to get x^{2} = 9/(y  2) I have an expression where x can be negative. Hence in reply to your question of how you solve x = 3 / sqrt (y  2) for y, you square both sides but when you square you need to keep track of any restrictions that are contained in the original form. Hence I have
The final form of the inverse has the property that x can't be zero but that is already contained in the restriction that x > 0 so the domain of the inverse is (0, ∞) and hence the range of the function y = 3 / sqrt (x2) is (0, ∞). I hope this helps,  


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