How do you find the domain of a function?

Question

here are a couple of the problems I am facing.

f(x) = 5x^2 + 2x - 1


f(x) = 3y / x + 5

Answer 1

f(x) = 5x^2 + 2x - 1
Just ask yourself what values can x be. It should be clear that x can be any real number so the domain of the above function is (-infinity , +infinity)


f(x) = 3y / (x + 5)
Here, you should observe that x cannot be equal to -5 as that would result in division by zero whicch is a no-no. So the domain is all the real numbers except -5

Other things you should look out for is square roots. Any value of x that would result in taking the square root of a negative number must be exclude from the domain.

Answer 2

x is th domain, y is the range. sub f(x) for a number like 2 so;

f(2)=5(2)^2+2(2)-1

answer is the domaiun

Answer 3

first one, you have to graph it and the domain is all real numbers. the second one, the denominator can't equal 0 so domain is all real numbers except -5