If f : R → R and g : R → R are given by f(x) = x and g(x) = [x] for each x ∈ R, then x ∈ R : gfx ≤ fgx is equal to
Z ∪ - ∞, 0
- ∞, 0
Z
R
If f(x) = 1x + 22x - 4 + 1x - 22x - 4 for x > 2, then f(11) is equal to
76
56
67
57
If efx = 10 + x10 - x, x ∈ - 10, 10 and f(x) = kf200x100 + x2, then k is equal to
0.5
0.6
0.7
0.8
A.
We have,efx = 10 + x10 - x, x ∈ - 10, 10fx = 10 + x10 - xGiven that, fx = kf200x100 + x2⇒ log10 + x10 - x = klog10 + 200x100 + x210 - 200x100 + x2 = klog1000 + 10x2 + 200x1000 + 10x2 - 200x = klogx2 + 100 + 20xx2 + 100 - 20x = klogx + 10210 - x2 = 2klog1 0+ x10 - x⇒ log1 0+ x10 - x = 2klog1 0+ x10 - x∴ 2k = 1 ⇒ k = 12 = 0.5
Let a, b, and c be such that 11 - x1 - 2x1 - 3x = a1 - x + b1 - 2x + c1 - 3x then, a1 + b3 + c5 is equal to
115
16
15
13
If 0 < y < 213 and xy3 - 1 = 1, then 2x + 23x3 + 25x5 + ...is equal to :
logy32 - y3
logy31 - y3
log2y31 - y3
logy31 - 2y3
If f : N → Z is defined byf(n) = 2 if n = 3k, k ∈ Z10 if n = 3k + 1, k ∈ Z 0 if n = 3k + 2, k ∈ ZThen, n ∈ N : fn > 2 is equal to
{3, 6, 4}
{1, 4, 7}
{4, 7}
{7}
The value of 42 + 42 + 42 + ... is equal to
7
- 6
5
4
If log27log3x = 13, then the value of x is
3
6
9
27
x = 123 + 13, then x2 - 1x - x2 - 1
1
2
12
If a, b, c ≠ 0 and belong to the set to {0, 1, 2, 3, ..., 9}, then log10a + 10b + 102c10- 4a + 10- 3b + 10- 2c is equal to