Eamcet - Maths - Functions

If f : R → R is continuous such that f(x + y) = f(x) + f(y), ∀x∈R, y∈R, and f(1) = 2 then f(100) =

A.  100

B.  50

C.  0

D.  200

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If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=

A.  0

B.  1

C.   5   d) 15/2

D.  15/2

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Let f(x)=-2sinx, if x≤-π/2; f(x)=a sinx+b,if –π/2

A.  a=0, b=1

B.  a=1,b=1

C.  a=-1,b=0

D.  a=-1,b=1

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The domain of √[x-1/2-x] is

A.  (1, 2]

B.  [1, 2)

C.  (-∞, 1) U [2, ∞)

D.  (-∞, 1] U (2, ∞)

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If fn(x)= (tan x/2)(1+sec x)(1+2 sec x)…….(1+sec 2n x) then the following is not true?

A.  f2(π/16)=1

B.  f3(π/32)=1

C.  f4(π/64)=1

D.  f5(π/128)=0

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The range of f(x)=10- |3-2x| is

A.   (10, ∞)

B.  [10, ∞)

C.  (-∞, 10)

D.  (-∞, 10]

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Domain of log(x-2)/√3-x is

A.  (2, 3)

B.  [2, 3)

C.  (2, ∞)

D.  (-∞, 3)

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If A={1,2, 3}, B= {a, b, c, d}, f={(1,a), (2, b), (3, d)}, then f is

A.  mapping

B.  one one

C.  onto

D.  one-one-onto

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The function y=f(x) satisfying the condition f(x+1/x)=x3+1/x3 is

A.  f(x)=x2

B.  f(x)=x2-2

C.  f(x)=x2+2 

D.  f(x)=x3-3x

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If f: R-{5/2}→R-{-1} defined by f(x)=2x+3/5-2x then f-1(x)=

A.  5x-3/2+2x

B.  4x+3/x+1

C.  7+5x/3-2x

D.  2-5x/3+7x

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If f(x)=3x-7/5x-3 then (fof)(x)=

A.  x

B.  –x

C.  3x

D.  f(x)

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The domain of the function √1/cos |x| is

A.  R-{π/2}

B.  R-{π/2, 3π/2}

C.  R-{(2n+1)π/2: n? Z}

D.  R-{nπ: n? Z}

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Consider the function f(x)=x sin(1/x),x≠0 and f(0) =0,then

A.  it is continuous for all real values of x

B.  it is discontinuous everywhere

C.  f(x) exists and discontinuous at x=π/2

D.  none of these

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If f(x)=[x], g(x)=x-[x]then which of the following functions is the zero functions

A.  (f+g)(x)

B.  (fg)(x)

C.  (f-g)(x)

D.  (fog)(x)

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If f: R→R,, g: R→R, are defined by f(x)=4x-1, g(x)=x3+2, then gof(a+1/4)=

A.  43

B.  345

C.  a3+2

D.  a2-1

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The domain of 1/ log(1-x) is

A.  (-∞, -1)

B.  (1, ∞)

C.  (-∞, 0) U (0, 1)

D.  (-∞, 0) U (0, 1]

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The function f(x) = x/√1-x2 and g(x)=x/√1+x2, find fog(x).

A.  x

B.  x2

C.  x/√1-x2

D.  none of these

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If  f(x)=1og(cos x),  then  domain f.=

A.  {x: 2nπ-π/2 < x< 2nπ+ π/2, n ? Z}

B.  {x: 2nπ< x

C.  {x: x? (-∞, ∞)}

D.  none

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If f={(a, 1), (b, -2), (c, 3)}, g={(a, -2), (b, 0), (c, 1)} then f2+g2=

A.  {(a, -1), (b, -2), (c, 4)}

B.  {(a, 3), (b, -2), (c, 2)}

C.  {(a, -4), (b, -4), (c, 9)}

D.  {(a, 5), (b, 4), (c, 10)}

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A={-1, 0, 1, 2}, B= {2, 3, 6,}If f from A into B defined by f(x)=x2+2, then f  is

A.  function

B.  one one

C.  onto

D.  one one onto

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If f(x)=x3-x, g(x)=sin 2x, then

A.  g{f(2)}= sin 2

B.  g{f(1)}=1

C.  f{g(π/12)}=-3/8

D.  f{f(1)}=2

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If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

A.  a

B.  x

C.  xn

D.  an

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If  f(x)=αx+β and f={(1, 1), (2,3), (3,5), (4, 7)} then the values of α, β are

A.  2, -1

B.  -2, 1

C.  3, -1

D.  -2, -1

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If y=x2+2x+1/x2+2x+7, then inverse function x is defined only when

A.  0

B.  0

C.  0≤y

D.  0≤y≤1

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if f: [0, ∞)→R defined by f(x)=x2, then f is

A.  a function

B.  one one

C.  onto

D.  one one onto

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If f:[0, ∞)→[0, ∞) defined by f(x)=x2, then f is

A.  a function

B.  one one

C.  onto

D.  one one onto

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The domain of Sin-1 log2 (x2/2) is

A.  [-2, -1]

B.   [1, 2]

C.  [-2, -1] U [1, 2]

D.  (0, ∞)

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The domain of √3+x + √3-x/x is

A.  [-3, 3]

B.  (-3, 0) U (0, 3)

C.   [-3, 0) U (0, 3]

D.  R

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If f(x)=1/2[3x+3-x], g(x)=1/2[3x-3-x], then f(x) g(y)+f(y)g(x)=

A.  f(x+y)

B.  g(x+y)

C.  2f(x)

D.  2g(x)

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The domain of log10 (x3-x) is

A.  (-1, 0) U (1, ∞)

B.  (-∞, -1) U (1, ∞)

C.  (-∞, 0) U (1, ∞)

D.  (-∞, -1) U (0, ∞)

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