Question

Is this function continuous on the given interval ?f(x)=6x+x^-1 on [-2,2]

Answer 1

can x^-1 be zero?

Answer 2

yes I think so

Answer 3

definition:\[x^{-1}=\frac1x\]

Answer 4

ok

Answer 5

what does 1/0 equal ?

Answer 6

undefined. x can't equal zero

Answer 7

good, then all we have to do is see if x=0 is in the interval; if so, then it is not continuious

Answer 8

You can't have x equal zero, because 1 cannot be divided by zero, so its not continuous, since it does not go through zero. Right?

Answer 9

correct

Answer 10

we have to "jump" over zero to get from -2 to 2

Answer 11

exactly. Thanks.