Question

Determine the intervals on which f(x)=sqrt((x+1)/x) is continuous

Answer 1

\[f(x)=\sqrt{\frac{x+1}{x}}\]?

Answer 2

yes

Answer 3

this function, like almost all that you know, is continuous on its domain, so what you are really being asked for is the domian of this function. that boils down to finding where the expression inside the square root is greater than or equal to zero.
of course you have to exclude zero as well, because you may not divide by zero

Answer 4

oh okay

Answer 5

i.e. you need to solve
\[\frac{x+1}{x}\geq 0\]

Answer 6

is that ok?

Answer 7

I think so, wouldn't it be 1>infinity

Answer 8

oh no

Answer 9

\[\frac{x+1}{x}\geq 0\] this thing changes sign at both 0 and 1
it is postive if \(x<-1\) or if \(x>0\)

Answer 10

sorry i meant changes sign at \(x=-1\) and at \(x=0\)

Answer 11

i think i found out is it (-infinity,-1)U(0,infinity)

Answer 12

yes, that is it although the -1 should be included

Answer 13

well maybe not because it would not be continuous from the right, so stick with your answer

Answer 14

oh okay thank you

Answer 15

your answer is correct

Answer 16

yw