A few math questions!!?

Question

Thanks so much in advance!!!
1) Find the domain of the function.

F(X) √ 2x-14

2) Find the domain of the given function.

F(X) = x-10 / x^3+9x

Thanks so much!!!
I had been working these out for some time and seemed to have a hard time.
Your answers really helped me understand it all. Thanks!!!!

Answer 1

for the first one, if the radical is over the whole quantity then:
x can not be less than 7 because anything less like a 6, for instance would force us to find the square root of (12-14) or -2 and we don't have the root of negative numbers, so x has to start at 7 and go to + infinity, anything less is not defined.

for the second function, x cannot equal zero because it will result in a number divided by zero which is undefined.

Answer 2

1.) f(x) = √(2x-14)

might help to look at this problem from a simplified view
pull out a two from the 2x-14
f(x) = √2x-14 = √2 * √x-7
now you might be able to see that x cannot be less than 7. The square root of a negative number is undefined in general mathematics. There is an imaginary number for every negative square root but that is not included in a function like this. so domain is:
x >= 7

2.) F(X) = (x-10 )/ (x^3+9x)

in a division function like this you wanna watch out for a divide by zero. Don't let the function be undefined.
This function will be undefined if x = 0
plug in zero and get -10/0. undefined

domain: x ≠ 0

Answer 3

1. for √, radicand must be ≥ 0, so 2x-14 ≥ 0, 2x ≥ 14, x ≥ 7.

2. for rational expressions, cannot divide by 0, so x³ + 9x <> 0, x(x²+9) <> 0, x <> 0.