The inverse of the function f(x) = fx = 10x -

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The equation ex - x - 1 = 0 has, apart from x = 0

  • one other real root

  • two real roots

  • no other real root

  • infinite number of real roots


22.

Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B ?

  • {(1, 2), (2, 3), (3, 4), (2, 2)}

  • {(1, 2),(2, 3), (1, 3)}

  • {(1, 3), (2, 3), (3, 3)}

  • {(1, 1), (2, 3), (3, 4)}


23.

If y = 21logx8, then x is equal to

  • y

  • y2

  • y3

  • None of these


24.

The domain of the function

fx = log10x - 4 + 6 - x is

  • [4, 6]

  • - , 6

  • (2, 3)

  • None of these


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25.

The inverse of the function f(x) = fx = 10x - 10- x10x + 10- x is

  • log102 - x

  • 12log101 +x1 - x

  • 12log102x - 1

  • 14log2x2 - x


B.

12log101 +x1 - x

Let y = f(x)  x = - 1yThen, y = 10x - 10- x10x + 10- x 10x + 10- xy = 10x - 10- x      102x + 1y = 102x - 1      102xy - 1 = - y + 1   102x = y + 11 - y      2x = log101 + y1 - y        x = 12log101 + y1 - y f- 1y = 12log101 + y1 - y

Hence, the required inverse function is 12log101 + x1 - x


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26.

The number of solutions of log2x - 1 = 2log2x - 3

  • 2

  • 1

  • 6

  • 7


27.

If fx = x - 1x + 1, then f(2x) is

  • fx + 1fx + 3

  • 3fx + 1fx + 3

  • fx + 3fx + 1

  • fx + 33fx + 1


28.

∼ (P ∨ q) v ( ∼ p ∧ q) is logically equivalent to

  • - p

  • p

  • q


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29.

Given, fx = log1 + x1 - x and gx = 3x + x31 +3x2, then fog(x) equals

  • [f(x)]3

  • - f(x)

  • 3f(x)

  • None of these


30.

The relation on the set A = {x : x < 3, x  Z} is defined by R = {(x, y) : y = x, x  - 1} Then, the number of elements in the power set of R is

  • 8

  • 16

  • 32

  • 64


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