CAT 2021 Slot 3 · Quant · Question 22
CAT 2021 Slot 3 previous year question on Functions, with the answer and a step-by-step solution.
If f\left( x \right)={x}^{2}-7x and g\left( x \right)=x+3, then the minimum value of f\left( g\left( x \right) \right)-3x is
- A-20
- B-15
- C-12
- D-16
Pick an option, then check.
Answer & solution
Answer: Option D
Compose first, then simplify before minimising.
f\left( g\left( x \right) \right)={\left( x+3 \right)}^{2}-7\left( x+3 \right)={x}^{2}+6x+9-7x-21={x}^{2}-x-12.
So f\left( g\left( x \right) \right)-3x={x}^{2}-4x-12.
Completing the square, {x}^{2}-4x-12={\left( x-2 \right)}^{2}-16.
A square is never negative, so the least value is -16, reached at x=2.
More Functions questions
- 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
- 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
Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.