Let f : R → R be the function defined by f(x) = x&

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 Multiple Choice QuestionsMultiple Choice Questions

311.

If f(x) = 2x - 1x +5; x  - 5, then f-1(x) is equal to

  • x + 52x - 1, x  12

  • 5x + 12 - x, x  2

  • x - 52x + 1, x  12

  • 5x - 1x - 2, x  2


312.

A· {(B + C) x (A + B + C)} equals

  • [A B C]

  • [B A C]

  • 0

  • 1


313.

Which is incorrect ?

  • (AB)' = B'A'

  • ABθ = BAAθ

  • AB = B A

  • AB-1 = B-1A-1


314.

Cube root of 18 by using Newton-Raphson method will be

  • 2.26

  • 2.620

  • 2.602

  • None of these


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315.

The difference of the numbers (1100110011)2 and (1101001011)2 in binary system is

  • (100000)2

  • (101010)2

  • (11000)2

  • (10111)2


316.

If the function f · f . [1, )  [1, ) is defined by f(x) = 2x(x - 1), then f-1(x) is defined by

  • 12xx - 1

  • 121 ± 4log2x

  • 121 - 1 - 4log2x

  • None of these


317.

By Newton-Raphson method, the positive root of the equation x4 - x - 10 = 0 is

  • 1.871

  • 1.868

  • 1.856

  • None of these


318.

Which of the following function is inverse of itself

  • fx = 1 - x1 + x

  • g(x) = 5log(x)

  • h(x) = 2x(x - 1)

  • None of the above


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319.

Let f : R  R be the function defined by f(x) = x - 3 , x  R. Then f-1(x) = ?

  • x + 3

  • x2 + 3

  • x + 32

  • x2 + 32


B.

x2 + 3

We have,          f(x) = x - 3,  x  RWe know that, ff-1x = x = f-1fx   ff-1x = f-1x - 3         x = f-1x - 3       x2 = f-1x - 3       squaring both sides f-1x = x2 + 3


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320.

Let Z denote the set of integers define f : Z  Z by f(x) = x2, x is even0,   x is odd, then f is

  • onto but not one-one

  • one-one but not onto

  • one-one and onto

  • neither one-one nor onto


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