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*Answer can only contain numeric values

Try yourself:For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

[2019 TITA]

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*Answer can only contain numeric values

Try yourself:Consider a function f(x + y) = f(x) f(y) where x , y are positive integers, and f(1) = 2. If f (a + 1) + f (a + 2) + ..... + f(a + n) = 16 (2^{n} - 1) then a is equal to.

[2019 TITA]

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*Answer can only contain numeric values

Try yourself:Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals

[2019 TITA]

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*Answer can only contain numeric values

Try yourself:If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals.

[2018 TITA]

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*Answer can only contain numeric values

Try yourself:Let f(x) = min{2x^{2}, 52 - 5x}, where x is any positive real number.Then the maximum possible value of f(x) is

[2018 TITA]

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*Answer can only contain numeric values

Try yourself:Let f(x) = max{5x, 52 - 2x^{2}}, where x is any positive real number.Then the minimum possible value of f(x) is

[2018 TITA]

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*Answer can only contain numeric values

Try yourself:If f_{1}(x) = x^{2} + 11x + n and f_{2}(x) = x, then the largest positive integer n for which the equation f_{1}(x) = f_{2}(x) has two distinct real roots, is:

[2017 TITA]

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Try yourself:Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

[2017]

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Try yourself:If f(x) = 5x + 2 / 3x − 5 and g(x) = x^{2} – 2x – 1, then the value of g(f(f(3))) is:

[2017]

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Try yourself:Let f(x) = x^{2} and g(x) = 2^{x}, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

[2017]

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*Answer can only contain numeric values

Try yourself:If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

[2017 TITA]

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