AIEEE Discussion Forum, Questions

Hi all,

Just thought I would share a few good questions in sets, relations and functions

1. Domain of definition for the function 4/sqrt((9-x^2)) + Ln (x^3-x) is
a. (-3,0) U (1,3)
b. (-1,0) U (1,3)
c. (-1,3)
d. (-3,-1) U (0,3)

2. The range of the function (x^2+4x+7)/(x^2+4x+6) is
a. [1,3/2)
b. (1,3/2]
c. [1,3/2]
d. [0,3]

3. f(x) is defined as x^(1/x), x belongs to the set of natural numbers. The maximum value of f(x) is reached when x equals
a. 2
b. 3
c. 7
d. F(x) is a non-decreasing function. It has not definable maximum

4. F(x) = x-[x], where [x] is the largest integer lesser than or equal to x, g(x) = x + abs(x), then
a. The union of the range of f(x) and g(x) is (0,1)
b. Neither f(x) nor g(x) can be negative for any x
c. g(x)+g(-x) = 2x
i. All three are true
ii. B and c are true
iii. Only b is true
iv. Only c is true

5. Domain of the function f(x)= Inv-sin(x-4)/sqrt(16-x^2) + Inv-cos(3-x) is
a. (3,5)
b. [2,3] U [4,5]
c. [3,4)
d. (3,4)
e. None of the above

I think all of these are reasonable questions, or questions with a difficulty level appropriate for AIEEE. Happy solving