Inverse of function f(x) = 10x - 10- x10x&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

271.

The value of the expression 1 . (2 - w)(2 - w2) + 2 . (3 - w)(3 - w2) + ... + (n - 1)(n - w2), where w is an imaginary cube root of unity is

  • nn + 122

  • nn + 122 - n

  • nn + 122 + n

  • None of these


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272.

Inverse of function f(x) = 10x - 10- x10x + 10- x is

  • log10(2 - x)

  • 12log101 + x1 - x

  • 12log102x - 1

  • 14log102x2 - x


B.

12log101 + x1 - x

Let fx = y, then 10x - 10- x10x + 10- x = y 102x - 1102x + 1 = y          102x = 1 + y1 - y                x = 12log101 + y1 - y       f-1y = 12log101 + y1 - y        f-1x = 12log101 + x1 - x


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273.

Let f : R - {x}  R be a function defined by f(x) =  x - mx - n, where m  n. Then

  • f is one-one onto

  • f is one-one into

  • f is many one onto

  • f is many one into


274.

The domain of definition of function fx = 1 +2x +4- 0.52 - x +4- 0.5 + x + 40.5 + 4x + 40.5 is

  • R

  • (- 4, 4)

  • R+

  • - 4, 0  0, 


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275.

If f(x) = 4x4x + 2, then f197 + f297 + ... + f9697 is equal to

  • 1

  • 48

  • - 48

  • - 1


276.

Let a relation R be defined on set of all real numbers by a R b if and only if 1 + ab > 0. Then, R is

  • reflexive, transitive but not symmetric

  • reflexive, symmetric but not transitive

  • symmetric, transitive but not reflexive

  • an equivalence relation


277.

If xyx + y = 23, yzy + z = 65, xzx + z = 34, then (x, y, z) is equal to

  • (1, 2, 3)

  • (2, 1, 3)

  • (3, 1, 2)

  • (3, 2, 1)


278.

Let f(x) = 12 - tanπx2, - 1 < x < 1 and g(x) = 3 + 4x - 4x2, then dom(f + g) is given by

  • 12, 1

  • [12, - 1)

  • [ - 12, 1)

  • - 12, - 1


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279.

Let the functions f, g, h are defined from the set of real numbers R to R such that

fx = x2 - 1, gx = x2 + 1 andhx = 0, if x < 0x, if x  0

then ho(fog)(x) is defined by

  • x

  • x2

  • 0

  • None of these


280.

If f(x) = cos(log(x)), then f(x)f(y) - 12fxy + fxy has the value :

  • - 1

  • 12

  • - 2

  • zero


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