Help me solve this please?

Question

Let
f(x) = -6 x - 3.
Use interval notation to indicate where f(x) is continuous.

Interval(s) of Continuity: ____


Let f(x)= [3/x+4]
Use interval notation to indicate where f(x) is continuous.

Interval(s) of Continuity: ____

Answer 1

The fist one is all reall numbers so that would be (-infinity, infinity)

the second one would be (-infinity,-4) (-4, Infinity)
so that is all numbers except -4 becasue you cannot have a zero in the denominator.

Answer 2

Hi,
For polynomials, which is what the first problem is, any real number can be used. So, the answer is:
(-oo, oo) Where I've used the symbol oo for infinity.

Problem 2:
If there are variables in the denominator, we're going to have continunity problem. So, set the term in the demoninator equal to zero and solve for x and that's a number that is not in the domain, that is it won't work in the expession.
So, it's not clear from the way you have your problem written if you intend f(x) = (3/x) +4 or 3/(x+4). So, let's do both.
f(x) = (3/x) +4
x = 0
So, we must exclude 0 from the interval where the function is continuous.
(-oo, 0)U(0, oo) Where again oo represents infinity.

Now f(x) = 3/(x+4)
x+4 = 0
x = -4
(-oo, -4)U(-4, oo)

Hope this helps.
FE