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nysnowboard
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9. Let the function h be defined by h(x) = sqrt(x) + 2. If 3 h(v) = 18, then which one of the following is the
value of h(v/4)?
(A) -4
(B) -1
(C) 0
(D) 2
(E) 4
I get two possible solutions (both among the answer choices unfortunately), but the official solution only gives one. I can't figure out why (C) and (E) are both not equally valid answer choices... can anyone help me?
EDIT: Problem solved: Once again, I took a second look at the problem and realized, the graph of y = sqrt(x) + 2 is only defined in the range y >= 2. Unfortunately in the heat of the moment, I missed this insight (seems to happen to me far too often with this test). So once again, I will leave this up in the hopes that it will keep other people from making the same mistake....
[spoiler]
3 h(v) = 18
h(v) = 6
h(v) = sqrt(v) +2
6 = sqrt(v) + 2
4 = sqrt(v)
16 = v
h(v/4) = h(16/4) = h(4)
h(4) = sqrt(4) +2
= (+,-)2 + 2
= 2+2 = 4 -2+2= 0
I see both C and E as valid answers.
[/spoiler]
value of h(v/4)?
(A) -4
(B) -1
(C) 0
(D) 2
(E) 4
I get two possible solutions (both among the answer choices unfortunately), but the official solution only gives one. I can't figure out why (C) and (E) are both not equally valid answer choices... can anyone help me?
EDIT: Problem solved: Once again, I took a second look at the problem and realized, the graph of y = sqrt(x) + 2 is only defined in the range y >= 2. Unfortunately in the heat of the moment, I missed this insight (seems to happen to me far too often with this test). So once again, I will leave this up in the hopes that it will keep other people from making the same mistake....
[spoiler]
3 h(v) = 18
h(v) = 6
h(v) = sqrt(v) +2
6 = sqrt(v) + 2
4 = sqrt(v)
16 = v
h(v/4) = h(16/4) = h(4)
h(4) = sqrt(4) +2
= (+,-)2 + 2
= 2+2 = 4 -2+2= 0
I see both C and E as valid answers.
[/spoiler]
