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CAT Exam  >  CAT Questions  >  A function f(x), defined for real numbers, sa... Start Learning for Free
A function f(x), defined for real numbers, satisfies the following properties. f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?
    Correct answer is '1'. Can you explain this answer?
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    A function f(x), defined for real numbers, satisfies the following pro...
    Solution: f(x) + 4 < f(x + 4) < f(x + 3) + 1 <f( x+2 ) + 2 < f { x + 1) + 3 < f(x ) + 4
    We can see that the equality holds for all x. f { x + 1) = f(x) + 1
    . g(2008) = f(2008) + 1 - 2008 = f(2007) + 1 - 2007 = ... = f(1) + 1 - 1 = 1
    g(2008) = 1 Answer: 1
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    Most Upvoted Answer
    A function f(x), defined for real numbers, satisfies the following pro...
    Explanation:

    Given properties of f(x):
    - f(1) = 1
    - f(x + 4) = f(x) + 4
    - f(y + 1) = f(y) + 1

    Relationship between f(x) and g(x):
    - g(x) = f(x) + 1 - x
    - g(2008) = f(2008) + 1 - 2008

    Solving for g(2008):
    - g(2008) = f(2008) + 1 - 2008
    - g(2008) = f(2004 + 4) + 1 - 2008 (using f(x + 4) = f(x) + 4)
    - g(2008) = f(2004) + 4 + 1 - 2008 (using f(x + 4) = f(x) + 4)
    - g(2008) = f(2000 + 4) + 4 + 1 - 2008
    - g(2008) = f(2000) + 8 + 1 - 2008
    - g(2008) = f(1999 + 1) + 8 + 1 - 2008 (using f(y + 1) = f(y) + 1)
    - g(2008) = f(1999) + 1 + 8 + 1 - 2008 (using f(y + 1) = f(y) + 1)
    - g(2008) = f(1) + 1 + 8 + 1 - 2008
    - g(2008) = 1 + 1 + 8 + 1 - 2008
    - g(2008) = 1
    Therefore, the value of g(2008) is 1.
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    A function f(x), defined for real numbers, satisfies the following properties.f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?Correct answer is '1'. Can you explain this answer?
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    A function f(x), defined for real numbers, satisfies the following properties.f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?Correct answer is '1'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A function f(x), defined for real numbers, satisfies the following properties.f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?Correct answer is '1'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f(x), defined for real numbers, satisfies the following properties.f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?Correct answer is '1'. Can you explain this answer?.
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