Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:
A function f: ℝ → ℝ maps each real number in the domain ℝ to a real number in the range ℝ. For each input x ∈ ℝ, there is a corresponding output f(x) ∈ ℝ.
Class 12 Maths Relations and Functions Chapter 1 for CBSE Exam 2024-25 covers relations between sets and various types of functions such as one-one and onto. It introduces concepts like domain and range of functions along with composite functions and inverse functions. This chapter builds essential skills for advanced mathematical concepts.
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Let A = {1, 2, 3} and B = {4, 5, 6, 7}.
Let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B.
1. Injective (One-to-one): Each element of A goes to a distinct element in B. There are no two elements of A going to the same element in B.
Therefore, f is injective.
2. Surjective (Onto):
Not all elements of B are covered by f. For instance, 7 is not mapped by any element of A.
Therefore, f is not surjective.
3. Bijective (One-to-one and Onto):
Since f is not surjective, it cannot be bijective.
4. Function:
f is a function since every element of A is related to exactly one element of B.
Therefore, the correct answer is: Injective function.
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