Recent content by 1+1=2

So if a function is one-to-one, then to find its range, one can simply invert and set its denominator equal to zero. However, if the function is not one-to-one, I must use translational techniques in order to determine range. P.S. I will investigate polynomial division and post #25 further...

This also leads to another question. In thinking about the process of inverting a function and finding a function's range. Using the function y=\frac{1}{x-3} The inverse is gotten by switching the x and y values and solving for y. y=\frac{1}{x-3} => x=\frac{1}{y-3}...

________________________________________________ Firstly, the method of piecewise has caused something to click for me in regard to the original function f(x) = x/lxl The original method proposed by Zondrina is to create a piecewise of the form: { x, x>0 {-x, x<0 This piecewise...

Domain: {xl x≠0} Range: [1,-1] or just 1 and -1, In f(x), all y values are either 1 or -1. The range contains no verticle y values greater than or less than 1 and -1. So maybe I should write this range as {yl y = 1 and -1} or [1]U[-1]? How would you specify that the range of a...

Okay, and suppose I have the function: f(x) = \frac{x}{|x-3|} In my head, I can simply say that Domain: x≠3 But, finding the range seems more complex. Do I automatically set up a piecewise form? I'm not even sure how I'd go about creating a peicewise function for this type of function.

Case #2 : x<0 So f(x) = x/|x| = x/(-x) = -1 D = {x\inℝ} R = {y=-1} ( Since for all possible x values, f(x) = -1 ) This seems fairly easy (with advice and thought), but it seems unlikely that correct range values would be as easily obtained (as plugging in a few x values and noticing...

Robert, appreciate the clarification, so would mean that y = 0 is in fact an accepted value for range?

eumyang, thanks, that makes sense. I follow the rationale. It makes sense that 0 ≠ \frac{x}{lxl}. Is there any analytical approach to figuring y = 0? Supposing a range of a more complex function is supposed to be found? How would I go about it? Villyer, thanks, how can I turn this...

Yes, jedish, that is what I understand the definition of range to be, thus, so how do I find those possible y values? Robert, why not y = 0?

Homework Statement Find the domain and range of the function: F(x) = \frac{x}{lxl} Homework Equations ? The Attempt at a Solution domain is all x such that x ≠0 range: do i have to make this into a piecewise function, if so, how?