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Functions slowing down your pace of CAT preparation online? F(x), g(x) not letting you move forward to other topics? Don't worry! You are not alone! This happens to the best of us and one of the best ways to get out of this constant loop of fear is to practice CAT previous year paper. They back you up with questions and topics you can expect in the CAT Question Paper. Ace your preparation for the Quantitative Aptitude section of the CAT exam by practicing this question from functions taken from CAT 2020 Question paper.

Question 14 : Let f(x) = x2 + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

  1. 16
  2. 1
  3. 4
  4. 0

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Explanatory Answer

f(x+1) = f(x+1)2 + a(x+1) + b
f(x-1) = f(x-1)2 + a(x-1) + b
g(x) = (x+1)2 + a(x+1) + b - (x-1)2 - a(x-1) – b
= 4x + 2a
g(20) = 72 = 4(20) + 2a
a = - 4
x2 - 4x + b ≥ 0
(x-2)2 +b – 4 ≥ 0
Value of b is at least 4


The question is "Let f(x) = x2 + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is"

Hence, the answer is, "4"

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