Find the domain of the function.

Question

f(x) = sqrt 6-x
A. (-∞, 6) (6, ∞)
B. (-∞, sqrt6 ) (sqrt 6 , ∞)
C. (-∞, sqrt6]
D. (-∞, 6]

Answer 1

you know that √n must have n >= 0

SO, you need (6-x) >= 0

Now what do you think?

Answer 2

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

Answer 3

So, C?

Answer 4

Or d?? Actually, i think its D. Am i correct?

Answer 5

D looks good to me.

Answer 6

Ok, thanks!