Relations and Functions

Q. If A = {1, 2, 3} and B = {a, b}, how many one-to-one functions can be defined from A to B?

Solution

A one-to-one function cannot exist from a larger set A to a smaller set B.

Correct Answer: A — 0

Q. If A = {1, 2, 3} and B = {x, y}, how many functions can be defined from A to B?

Solution

Each element in A can map to any of the 2 elements in B. Therefore, the total number of functions is 2^3 = 8.

Correct Answer: C — 8

Q. If A is a subset of B and B is a subset of C, which of the following is true?

Solution

Since A is a subset of B and B is a subset of C, it follows that A is also a subset of C.

Correct Answer: A — A is a subset of C

Q. If f(x) = 2x + 3 and g(x) = x^2, what is g(f(2))?

Solution

First, calculate f(2) = 2(2) + 3 = 7. Then, g(7) = 7^2 = 49.

Correct Answer: B — 28

Q. If f(x) = 3x - 5 and g(x) = x + 4, what is (f ∘ g)(1)?

Solution

First, calculate g(1) = 1 + 4 = 5. Then, f(5) = 3(5) - 5 = 10.

Correct Answer: A — 0

Q. If f(x) = 5x + 1, what is the value of f(0)?

Solution

f(0) = 5(0) + 1 = 1.

Correct Answer: B — 1

Q. If the function f(x) = x^2 - 4, what is f(-2)?

Solution

f(-2) = (-2)^2 - 4 = 4 - 4 = 0.

Correct Answer: C — 4

Q. If the relation R = {(1,2), (2,3), (3,4)} is a function, what is R(2)?

Solution

In the relation R, the pair (2,3) indicates that R(2) = 3.

Correct Answer: C — 3

Q. Which of the following is not a function?

Solution

A function cannot have two different outputs for the same input. The first option has two outputs for input 1.

Correct Answer: A — {(1,2), (1,3)}

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