Question

find the domain of the function f.use limits to describe the behaviour of f at valus of x not in its domain 1/x+3

Answer 1

plz explain me

Answer 2

For what value of x will you divide by 0?

Answer 3

?

Answer 4

\[1\div x+1\]

Answer 5

Cool.

\[f(x) = {1 \over x+3}\]

Where do you think will this function have a discontinuity? Aka, for what values of x is this function undefined?

Answer 6

-3

Answer 7

Yes. So, do you agree this function is defined for every value of x, except for -3?

Answer 8

yup

Answer 9

so ow to write end bhaviour

Answer 10

i am stuck with that

Answer 11

Then we can agree that the domain of the function is:

\[(-\infty,-3) \cup (-3, \infty)\]

Answer 12

That means x goes from -infinity to JUST before three, meaning every value smaller than -3. and then it unites with every value larger than -3 to infinity

Answer 13

thx slaaibak

Answer 14

thank u ver much

Answer 15

For the limits:

\[\lim_{x \rightarrow -3^-} { 1 \over x + 3} = -\infty\]

similarly

\[\lim_{x \rightarrow -3^+} { 1 \over x + 3} = \infty\]

and lastly

\[\lim_{x \rightarrow -3} { 1 \over x + 3} = Does NotExist\]

Answer 16

ok got u but what happens in this case