Sets, Relations & Functions
Functions
nta_pyq_2025_jan
Grade 11
Question:
The number of real solution(s) of the equation x + 3x + 2 = min{|x - 3|, |x + 2|} is: 2
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
x + 3x + 2 = min{|x - 3|, |x + 2|} 2 (3) 2 y = x + 3x + 2 3 9 9 2 y = x + 2( )x + - + 2 2 4 4 2 3 1 y = (x + ) - 2 4 2 1 3 y + = (x + ) 4 2 -3 -1 \Rightarrow Parabola vertex ( , ) 2 4 \Rightarrow By graph 2 solution possible
Correct Answer: 3