Strange: Defined or Undefined (1 Viewer)

[kpq_sniper017]

Something came to my head as I was doing some inverse trig. function questions:

Suppose:
f(x) = x²(1 + 1/x²)
then f(x) is undefined for x=0.

But then expand f(x), then:
f(x) = x² + 1
which is defined for all real x.

???
Can someone please explain this to me?
Am I missing the obvious somewhere?

 

[George W. Bush]

It's undefined at x=0, as the original function holds the restriction x=/=0, and just because you get a value by expanding it doesn't remove that restrinction.

For example, (x^2 - 4)/(x-2) is undefined at x=2, even though for all x=/=2, f(x) = x+2

 

[clerisy]

When sketching that function, then, is that where you sketch
f(x)=x + 1 as normal, but with an open circle at x=0?

 

[:: ck ::]

yup

 

[kpq_sniper017]

oh ic now....
so it'd just be the parabola x² + 1 with a discontinuity at x=0?

 

[Xayma]

Exactly, it would have no turning point either.

 

[kpq_sniper017]

hhhmm.....interesting.

just while i think of it:

if you had x²-1/x+1, would that just be the line y=x-1 except with a discontinuity at x=-1?

 

[George W. Bush]

yep...