Raymond B. answered • 01/23/23
Math, microeconomics or criminal justice
f(x) = (x^2 -1)/(x-1) = (x+1)(x-1)/(x-1) =x+1,
except x cannot =-1 as that makes the fraction undefined. for x =1, (1^2-1)/(1-1) = 0/0 which is undefined. Division by zero is never permitted.
f(x) is the line x+1 with a "hole" in it, a discotinuity at x=-1 or the point (-1,0)
the domain is all possible values of x, which is all real numbers, except -1. In interval notation x is in the interval
(-infinity, -1) U (-1, infinity)
the range is all possible values of y or f(x) which is all real numbers except 0. In interval notation the range is
(-infinity, 0) U (0, infinity)
"U" stands for Union of the two separate intervals.
the range includes all negative numbers and all positive numbers, but not zero.
f(x) =y can be >0, or <0 but not =0, that's the range
{x|x not = -1}
UNLESS you really meant
f(x) = x^2 - 1/x -1 which is actually the way you wrote it, but odds are you didn't mean it that way, as it's far more complicated
But if you did mean it that way, then
domain is all real numbers except 0, as 0 makes a denominator =0 which is undefined or 1.3 or .8
and the range is all real numbers except 0 and about 0.9
the graph is a curve with two disjoint sections
and a "hole" in each
at about (1.3,0) and (-.8, .9)
use a graphing calculator to see this far better
