Question

How do you find the domain of `f(x)=(x^2-4x+4)/(2sin(x))`?

Answer 1

`f(x)=(x^2-4x+4)/(2sinx), x in RR, x!=npi`/`x!=180n`

Explanation:

The domain of a function is all the values of `x` for which the function is defined. Since the function is a quotient, the only values it isn't defined for is when the denominator is equal to zero.

Since the denominator is a `sin` function, we know that it will be equal to zero whenever `x` is a multiple of `pi^"c"` or `180^"o"`. So we can write this as `x!=npi`.