CAT Functions previous year questions

12 Functions questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q22Let 3≤ x≤ 6 and [x² ]= [ x ]² , where [ x ] is the greatest integer not exceeding x . If set S represents all feasible…CAT 2025 Slot 1 · Quant · Functions
• Q4Let f ( x )=(x)/(2x-1) and g ( x )=(x)/(x-1) . Then, the domain of the function h ( x )=f ( g ( x ) )+g ( f ( x ) ) is…CAT 2025 Slot 2 · Quant · Functions
• Q11If f ( x )= (x²+3x ) (x²+3x+2 ) , then the sum of all real roots of the equation √(f ( x )+1)=9701 isCAT 2025 Slot 3 · Quant · Functions
• Q15For real values of x , the range of the function f ( x )=(2x-3)/(2x²+4x-6) isCAT 2025 Slot 3 · Quant · Functions
• Q4A function f maps the set of natural numbers to whole numbers, such that f ( xy )=f ( x )f ( y )+f ( x )+f ( y ) for…CAT 2024 Slot 2 · Quant · Functions
• Q20For any non-zero real number x , let f ( x )+2f ( (1)/(x) )=3x . Then, the sum of all possible values of x for which f…CAT 2024 Slot 3 · Quant · Functions
• Q22Suppose f ( x,y ) is a real-valued function such that f ( 3x+2y, 2x-5y )=19x , for all real numbers x and y . The…CAT 2023 Slot 3 · Quant · Functions
• Q12For any real number x , let ⌊x⌋ be the largest integer less than or equal to x . If sum_n=1^(N)⌊(1)/(5)+(n)/(25)⌋=25…CAT 2022 Slot 1 · Quant · Functions
• Q10Suppose for all integers x , there are two functions f and g such that f ( x )+f ( x-1 )-1=0 and g ( x )=x² . If f…CAT 2022 Slot 2 · Quant · Functions
• Q6Let r be a real number and f ( x )=2x-r if x≥ r , and f ( x )=r if x<r . Then, the equation f ( x )=f ( f ( x ) )…CAT 2022 Slot 3 · Quant · Functions
• Q13For all real values of x , the range of the function f ( x )=(x²+2x+4)/(2x²+4x+9) isCAT 2021 Slot 2 · Quant · Functions
• Q22If f ( x )=x²-7x and g ( x )=x+3 , then the minimum value of f ( g ( x ) )-3x isCAT 2021 Slot 3 · Quant · Functions