Sets, Relations & Functions
Functions
nta_pyq_2025_jan
Grade 11
Question:
Let f : [0, 3] \to A be defined by f (x) = 2x - 15x + 36x + 7 and g : [0, \infty) \to B be defined by g(x) = 2025 . 3 2 x 2025 x +1 If both the functions are onto and S = {x \in Z : x \in A or x \in B}, then n(S) is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
as f (x) is onto hence A is range of f (x) ′ (2) f (x) = 6x 2 - 30x + 36 = 6(x - 2)(x - 3) now f (2) = 16 - 60 + 72 + 7 = 35 f (3) = 54 - 135 + 108 + 7 = 34 f (0) = 7 hence range \in [7, 35] = A also for range of g(x) 1 g(x) = 1 - \in [0, 1) = B 2025 x + 1 s = {0, 7, 8, \ldots .35} hence n(s) = 30 x
Correct Answer: 2