Find the domain of the function.
f(x) = sqrt 6-x
A. (-∞, 6) (6, ∞)
B. (-∞, sqrt6 ) (sqrt 6 , ∞)
C. (-∞, sqrt6]
D. (-∞, 6]
you know that √n must have n >= 0
SO, you need (6-x) >= 0
Now what do you think?
The domain of a function is the set of all x's that can be substituted into the function and the function is defined. You are dealing with a square root. A sqrt will lead to a real number when the expression underneath the radical sign is NOT negative which can be written as >=0. So you'd get the inequality
84 - 6x >= 0
-6x >= -84 divide both sides by -6. REMEMBER that when you multiply or divide an inequality by a negative number, the
x<=14 inequality symbol must be reversed
So, C?
Or d?? Actually, i think its D. Am i correct?
D looks good to me.
Ok, thanks!
To find the domain of a function, you need to identify all the possible values that can be inputted into the function without resulting in an undefined output.
In this case, we have the function f(x) = √(6-x).
Notice that the function involves the square root operation. For the square root to be defined and have a real output, the expression inside the square root (6-x) must be greater than or equal to zero.
Setting the expression inside the square root to be greater than or equal to zero, we have:
6 - x ≥ 0.
Now, solve this inequality for x:
x ≤ 6.
Therefore, the domain of the function is all real numbers x such that x is less than or equal to 6.
This can be represented as:
D. (-∞, 6].