If f(x) = x + 1x - 1, then the value of

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 Multiple Choice QuestionsMultiple Choice Questions

231.

If f(1) = 1, f(2n) = f(n) and f(2n + 1) = {f(n)}2 - 2 for n = 1, 2, 3, ... , then the value of f(1) + f(2) + ... + f(25) is

  • 1

  • - 15

  • - 17

  • - 1


232.

In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three game is

  • 13

  • 24

  • 28

  • 52


233.

A function f satisfies the relation f(n) = f(n2) + 6 for n  2  and f(2) = 8. Then, the value of f(256) is

  • 24

  • 26

  • 22

  • 28


234.

If * is the operation defined by a b = ab for a, b  N, then (2 * 3) * 2 is equal to

  • 81

  • 512

  • 216

  • 64


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235.

The domain of the function f(x) x2 - 9/x - 3, if x  36,                          if x = 3 is

  • (0, 3)

  • - , 3

  • - , 

  • 3, 


236.

Let f(x) = x3 and g(x) = 3*. The values of A such that g[f (A)] = f[g(A)] are

  • 0, 2

  • 1, 3

  • 0, ± 3

  • 0, ± 3


237.

If fx + 12x - 1 = 2x, x  N, then the value of f(2) is equal to

  • 1

  • 4

  • 3

  • 2


238.

For all rest numbers x and y, it is known as the real valued function f satisfies f(x) + f(y) = f(x + y). If f(1) = 7, then r = 1100fr is equal to

  • 7 x 51 x 102

  • 6 x 50 x 102

  • 7 x 50 x 102

  • 7 x 50 x 101


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239.

If f(x) = x + 1x - 1, then the value of f(f(x)) is equal to

  • x

  • 0

  • - x

  • 1


A.

x

We have,fx = x + 1x - 1 ffx = fx + 1x - 1              = x+ 1x - 1 - 1x + 1x - 1 - 1              = x + 1 +x - 1x - 1 -x +1              = 2x2              = x


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240.

If fx = 1 - x1 + xx  - 1, then f-1(x) equals to :

  • f(x)

  • 1fx

  • - f(x)

  • - 1fx


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