What is the restriction for x?

Question

Problem :

f(x)= squareroot (x+6)/6+x

Answer 1

If I am reading your function correctly...
f(x) = [SQRT (x + 6)] / (6 + x)

The denominator cannot be zero. Therefore x <> -6

The number under the square root must be positive. Therefore, x + 6 >= 0; which implies x >= -6.

The first statement eliminates x = -6 from consideration.

Therefore, the restrictions are that x > -6.

Answer 2

x + 6 needs to be greater than or equal to zero so that you don't take the square root of a negative number. (I'm assuming you are only using reall numbers).
x+6 >= 0
x >= -6

Your domain is x>= -6

Answer 3

domain: all real numbers except x>=-6
This is to ensure that the denominator would not be equal to zero and that at x>=-6, the numerator would be imaginary number

Answer 4

x cannot equal negative 6

because you can't have a zero as the denominator. then it wouldn't be a function.

anything else should be okay.

so all real numbers EXCEPT negative 6

that's your domain.

restriction is the first sentence i said.