Subject: Domain and Range of a Function
Name: Michelle Mellott
Who is asking: Other
Question: How do you find the range of the following function:
I know the domain is x not equalled to -2, -3. How can one easily find the range?
In general it is not easy to find the range of a function. Finding the domain is usually easier but even this can be difficult at times. One way to find the range, or at least make an intelligent approximation, is to use some graphing program to graph the function and read the range from the graph. I tried this with your function
I had to plot it with different scales and look at various portions of the domain, but I was able to convince myself that the range is all y greater than or equal to zero together with all y less than or egual to some number between -20 and -25. Not a very satisfactory answer.
To find the inverse, interchange the roles of x and y to get
and then solve for y.
If x = 1 then y = -6/5 and if x is not 1 the general quadratic gives
Thus we get two values for y, one with the + sign and the other with he - sign. In either case the domain, which is the range of the function you started with, is all x such that x2 + 24x is greater than or equal to zero. Probably the easiest way to see which values of x make x2 + 24x 0 is to sketch the graph of y = x2 + 24x = x(x-24). The graph shows that x2 + 24x 0 when x -24 or x 0. Thus the range of
is all numbers which are either less than or equal to -24 or greater than or equal to 0.