If : R → R and g : R → R are defined by f(x) = x - [x] and g(x) = [x] for x ∈ R, where[x] is the greatest integer not exceeding x, then for every x ∈ R, f(g(x)) is equal to
x
0
f(x)
g(x)
If ax = by = cz = dw, the value of x1y + 1z + 1w is
logaabc
logabcd
logbcda
logcdab
B.
Given, ax = by = cz = dw⇒ x = ylogab = zlogac = wlogad⇒ y = xlogab, z = xlogac, w = xlogadNow x1y + 1z + 1w = xlogabx + logacx + logadx = xxlogabcd = logabcd
If : R→R and g : R→R are defined by fx = x and gx = x - 3 for x ∈ R, then gfx : - 85 < x < 85 is equal to
{0, 1}
{1, 2}
{- 3, - 2}
{2, 3}
Given that a, b ∈ 0, 1, 2, . . . , 9 witha + b ≠ 0 and that a + b10x = ab + b100y = 1000. Then,1x - 1y is equal to
1
12
13
14
If x = 127 + 17, then x2 - 1x - x2 - 1 is equal to
2
3
4
∑k = 1∞1k!∑n = 1k2n - 1 is equal to
e
e2 + e
e2
e2 - e
x ∈ R : 2x - 1x3 + 4x2 + 3x ∈ R equals
R - {0}
R - {0, 1, 3}
R - {0, - 1, - 3}
R - 0, - 1, - 3, +12
If f(0) = 0, f(1) = 1, f (2) = 2 and f(x) = fx - 2 + fx - 3 for x = 3, 4, 5, . . . , then f(9) = ?
10
log42 - log82 + log162 - . . = ?
loge2
1 + loge3
1 - loge2
For x ∈ R, the least value of x2 - 6x + 5x2 + 2x + 1 is
- 1
- 12
- 14
- 13