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
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
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
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
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
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
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
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}
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
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)
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
The domain of 1/ log(1-x) is
A. (-∞, -1)
B. (1, ∞)
C. (-∞, 0) U (0, 1)
D. (-∞, 0) U (0, 1]
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
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
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)}
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
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
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
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
if f: [0, ∞)→R defined by f(x)=x2, then f is
A. a function
B. one one
C. onto
D. one one onto
If f:[0, ∞)→[0, ∞) defined by f(x)=x2, then f is
A. a function
B. one one
C. onto
D. one one onto
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)
The domain of log10 (x3-x) is
A. (-1, 0) U (1, ∞)
B. (-∞, -1) U (1, ∞)
C. (-∞, 0) U (1, ∞)
D. (-∞, -1) U (0, ∞)