Find the domain of the function f(x) = (x² + 2x + 1) / (x² − 8x + 12).
R
R − {2, 6}
R − {−2, −6}
[2, 6]
Explanation: The denominator cannot be zero. x² − 8x + 12 = 0 factors to (x − 2)(x − 6) = 0. Thus, x cannot be 2 or 6. Domain is R − {2, 6}.
Question 2 of 6hard
The number of one-one functions from a 2-element set to a 3-element set is:
3
6
8
9
Explanation: Choose and arrange 2 images from 3 elements: 3×2=6.
Question 3 of 6hard
A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. This relation is:
Reflexive only
Symmetric only
Transitive only
Reflexive and Transitive
Explanation: It is reflexive because (1,1), (2,2), (3,3) are in R. It is not symmetric because (1,2) ∈ R but (2,1) ∉ R. It is transitive because there are no counterexamples to transitivity.
Question 4 of 6hard
If A={1,2,3} and B={a,b}, then number of functions from A to B is:
6
8
9
16
Explanation: Number of functions = 2³ = 8.
Question 5 of 6hard
Which of the following functions is neither even nor odd? f(x) = ?
x²
x³
x² + x
|x|
Explanation: An even function has f(−x) = f(x). An odd function has f(−x) = −f(x). For f(x) = x² + x, f(−x) = x² − x, which is neither f(x) nor −f(x).
Question 6 of 6hard
The domain of f(x) = 1 / √(9 − x²) is:
[−3, 3]
(−3, 3)
R − {−3, 3}
(−∞, −3) ∪ (3, ∞)
Explanation: For the function to be defined, 9 − x² > 0. Thus, x² < 9, which means −3 < x < 3. The domain is the open interval (−3, 3).
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