Question

What are the intervals in which the function is continuous.

y= (3/x+5)-2x

Answer 1

in other words, what makes this go bad that we have to avoid ...

Answer 2

there are 3 basic things that we must avoid in mathing at all times; never take the log of a number less than 0; never take the even root of a negative number; and never divide by zero

Answer 3

and this applies to the reals of course

Answer 4

which forbidden rule applies to this one?

Answer 5

never divide by zero

Answer 6

good, so when does: x+5 = 0 :)

Answer 7

-5

Answer 8

therefore x=-5 is banned:

(-inf,-5) U (-5,inf) is our domain

we have to pick one side or the other to have the interval of definition continuous

Answer 9

or simply; our intervals are:

(-inf,-5) ; (-5,inf)

Answer 10

So in order to find the intervals which a function continuous just make it equal zero