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}
f : [-6, 6] R is defined by f(x) = x2 - 3for x ∈ R, then(fofof) (-1) + (fofof) (0) + (fofof)(1) is equal to
f42
f32
f22
f2
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
If x2 + x + 1x2 + 2x + 1 = A + Bx + 1 + Cx + 12, then A - B is equal to
4C
4C + 1
3C
2C
∑k = 1∞1k!∑n = 1k2n - 1 is equal to
e
e2 + e
e2
e2 - e
If f : 2, 3→ R is defined by f (x) = x3 + 3x - 2, then the range f(x) iscontained in the interval
[1, 12]
[12, 34]
[35, 50]
[- 12, 12]
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
D.
f(0) = 0, f(1) = 1, f (2) = 2 Given, f(x) = fx - 2 + fx - 3, x = 3, 4, 5, . . . The given function is known as "Reccurrence function".put x = 3, f3 = f1 + f0 = 1 + 0 = 1put x = 4, f4 = f2 + f1 = 2+ 1 ⇒ 3put x = 5, f5 = f3 + f2 = 1 + 2 ⇒ 3put x = 6, f6 = f4 + f3 = 3 + 1 ⇒ 4put x = 7, f7 = f5 + f4 = 3 + 3 ⇒ 6put x = 8, f8 = f6 + f5 = 3 + 4 ⇒ 7put x = 9, f9 = f7 + f6 = 6 + 6 ⇒ 10Hence, f(9) = 10
log42 - log82 + log162 - . . = ?
loge2
1 + loge3
1 - loge2