Finding Domain of Function

Question

find domain of the function.

f(x) = 5x² + 2x - 1

g(x) = 1 - 2x²

s(y) = 3y

y + 5

g(y) = √y-10

Answer 1

A lot of times, it's easier to think about what x values you cannot use.

For f(x), there are no x values that are off limits so the domain is all real numbers, also written as -∞ < x < ∞ or as (-∞ , ∞)

For g(x), same answer as f(x).

For s(y) the denominator would be zero if y = -5 so -5 is off limits. So the domain is -∞ < y < -5 and -5 < y < ∞ or (-∞ , -5) ∪ (-5 , ∞)

For g(y), I'm assuming the -10 is underneath the square root. The issue here is that you can't take the square root of a negative number so y - 10 > 0 or y > 10 so the domain is 10 < y < ∞ or [10, ∞)