Finding Domain of functions?

Question

find domain of the functions and show work

f(x) = 5x² + 2x - 1

g(x) = 1 - 2x²

s(y) = 3y/y + 5

g(y) = √y-10

Answer 1

1) f(x) = 5x² + 2x - 1

It is a quadratic function. All quadratic functions have all real numbers as their domain.

The answer: all real numbers (R).

(-∞,∞)

2) g(x) = 1 - 2x²

Also a quadratic function.

The answer: all real numbers (R).

(-∞,∞)

3) s(y) = 3y/y + 5

This is a rational function that is linear in its lowest term, specifically, a horizontal line s(y)=8, with a caveat that y≠0.

The answer: (-∞,0)U(0,∞)

4) g(y) = √y-10

I assume (y-10) is under the square root.

This is a radical function. y-10≥0 hence y≥10.

The answer: [10,∞).