Find the domain of the function?

Question

Find the domain of the function
h(x) = (6 - x)(square root) + (x^ 2 - 4)(square root) .

a. (-∞,6]
b. (-∞,-6] ∪ [0,6]
c. (-∞,0] ∪ [2,6]
d. (-∞,-2] ∪ [2,6]
e. [2,6]

Answer 1

now 6-x>0
=> x<6
and x^2-4>0
=>x>2 or x<-2
the answer is D

Answer 2

Hello

I think you are saying

h = square root(6-x) + square root(x^ 2 - 4)

First of all we know that there can never be a negative under the square root.

So we have cant have anything smaller than a -2 or larger than 2, and larger than 6.

Combine these together we get

(-∞,-2] u [2,6]. This is option D.

Hope this helps

Answer 3

6 - x has a real square root iff 6 - x => 0
6 - x >= 0 // add x

6 >= x

x^2 -4 >= 0

Iff x^2 >= 4

or x>=2 or

x must fulfill 2 conditions:
i. x<=6
ii. X>=2 or x<=-2

If x<=-2 for sure, x<=6
If x>=2 we need to add the condition that x<=6

So, the correct answer is d.