The domain of the function f(x) = log2x + 3x2&nb

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 Multiple Choice QuestionsMultiple Choice Questions

221.

Let ϕx = bx - ab - a + ax - ba - b, where x  R and a and b are fixed real numbers with a  b. Then, ϕa + b is equal to

  • ϕab

  • ϕ- ab

  • ϕa + ϕb

  • ϕa - b


222.

The range of the function f(x) = x2 + 8x2 + 4, x  R is

  • - 1, 32

  • (1, 2]

  • (1, 2)

  • [1, 2]


223.

If n(A) = 1000, n(B) = 500 and if n(A  B) 1 and  nA  B = p, then

  • 500  p  1000

  • 1001  p  1498

  • 1000  p  1498

  • 1000  p  1499


224.

The domain of the function fx = sin-1x + 52 is

  • [- 1, 1]

  • [2, 3]

  • [3, 7]

  • [- 7, - 3]


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225.

If f(x) = x + 1 and g(x) = 2x, then f{g(x)} is equal to

  • 2(x + 1)

  • 2x(x + 1)

  • x

  • 2x + 1


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226.

The domain of the function f(x) = log2x +3x2 + 3x +2 is

  • R - {- 1, - 2}

  • R - {- 1, - 2, 0}

  • (- 3, - 1) ∪ (- 1, )

  • (- 3, ) - {- 1, - 2}


D.

(- 3, ) - {- 1, - 2}

Given function is f(x) = log2x +3x2 + 3x +2

Here, for existence of log

x + 3>0  x > - 3 x  - 3, and for existence of f(x)        x2 + 3x + 2  0 x + 1x +2  0                      x  - 1, - 2Hence, required domain of f(x) is- 3,  - - 1, - 2.


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227.

If * is defined by a * b = a - b2 and is defined by a b = a2 + b, where a and b are integers, then (3 4) * 5 is equal to

  • 164

  • 38

  • - 12

  • - 28


228.

The image of the interval [- 1, 3] under the mapping f : R  R given by f(x) = 4x3 - 12x is

  • [8, 72]

  • [0, 72]

  • [- 8, 72]

  • [0, 8]


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229.

If the operation is defined by a b = a2 + b2 for all real numbers a and b, then (2  3) 4 is equal to

  • 120

  • 185

  • 175

  • 129


230.

The domain of the function f(x) = 7 - 3x + logex is

  • 0 < x < 

  • 73  x < 

  • 0 < x  73

  • -  < x < 0


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