1.Locate the discontinuity of the function

Question

y=1/(1+sin x)
2.Suppose that f is a continuous function defined for all real numbers x and f(-5)=3 and f(-1)=-2 . If f(x) = 0 for one and only one value of x, then which of the following could be x?

Answer 1

#1: when is the denominator zero? When
1+sinx = 0
sinx = -1
x = 3π/2 + 2kπ

Since f(-5) > 0 and f(-1) < 0, f(x)=0 only for a single value of x between -5 and -1.

I assume the given choices included such a number.