What is the domain of the function defined by y = the square root of -5 - 9x ??

Answer 1

well darling
its our function ;
y = √-5 - 9x

as you know the square root just can accept Positive numbers and Zero . it means ;
-5 - 9x ≥ 0

Now just solve this inequality ;
-9x ≥ +5
x ≤ -(5/9)
OR
x ≤ - 0.55

Now Domain;
(-∞ , - 5/9 ] OR - ∞< x ≤ - 5/9

Good Luck Darling.

Answer 2

The domain is defined by the possible values of x that give a valid answer for y.
"the square root" or "√" can only accept positive (or nil) numbers so (-5-9x) should be positive (or nil).
You write:
-5-9x ≥ 0
-9x ≥ +5
9x ≤ -5
x ≤ -5/9 , this is the domain of your function.
Note that this also says that x can be as small as you want, or as small as -∞ (negative infinitee). As the ∞ (infinit) number can never be reached, we write
-∞ < x ≤ -5/9 , or give ] -∞ ; -5/9 ] as the domain of your function (note the way the square brackets are).

Answer 3

If it's a real-valued function, then -5-9x must be equal to or greater than 0 (else the √ doesn't exist) So
-5-9x ≥ 0 => -9x ≥ 5 => x ≤ -5/9 so -∞ < x ≤ -5/9


Doug