2007-01-19 06:58:49 · 7 answers · asked by webelieve04 2 in Science & Mathematics ➔ Mathematics
No, they are not.
The graph of g(x) looks identical to the graph of f(x) except for a hole at x=-2, where g(x) is undefined because that would cause division by zero.
Good question.
2007-01-19 07:02:57 · answer #1 · answered by bequalming 5 · 3⤊ 0⤋
Whenever x != -2 (i.e. x = 2 is false, or x does not equal 2), then (x^2 - 4)/(x+2) = x-2 indeed. But when x=-2, f(x) = f(2) = -4, whilst g(x) = g(2), which is undefined. So unless you restrict the domain of f to R-{2} (i.e. all real numbers but 2), no they are not the same function, if only for that reason alone.
2007-01-19 15:05:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Yes. If you factor g(x) = (x^2 -4)/(x+2) you will get ((x+2)(x-2))/(x+2) in which the (x+2) cancels in both the numerator and denominator.. So yes, the two functions given are the same.
2007-01-19 15:05:12 · answer #3 · answered by Robert B 2 · 0⤊ 2⤋
yes the two functions are the same. When you simplify the second function you get x-2.
2007-01-19 15:18:37 · answer #4 · answered by Scooter 2 · 0⤊ 0⤋
NO they are not the same.You can write the second as
g(x) =(x-2)*(x+2)/(x+2) and for EVERY X WHICH IS NOT -2 you can simplify but f(x) exists for every x and g(x) exist for every x except-2
2007-01-19 15:13:01 · answer #5 · answered by santmann2002 7 · 0⤊ 0⤋
yes =]
when u factor out the x^2-4 you get (x+2)(x-2) and then the (x+2) cancels out and leaves you with (x-2)
2007-01-19 15:02:59 · answer #6 · answered by Jackiee 3 · 0⤊ 2⤋
f(X) = x-2
g(x) = (x^2-4)/(x+2) = ((x-2)(x+2))/(x+2) = x-2
2007-01-19 15:04:59 · answer #7 · answered by Anonymous · 0⤊ 1⤋