A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to
–f(x)
f(x)
f(a) + f(a – x)
f(a) + f(a – x)
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
a function
reflexive
not symmetric
not symmetric
The range of the function 7-xPx-3 is
{1, 2, 3}
{1, 2, 3, 4, 5}
{1, 2, 3, 4}
{1, 2, 3, 4}
A.
{1, 2, 3}
The given function f(x) = 7-xPx-3 would be defined if
(i) 7 - x > 0 ⇒ x < 7
(ii) x - 3 > 0 ⇒ x > 3
(iii) (x - 3) < (7 - x)
⇒ 2x < 10 ⇒ x < 5
⇒ x = 3, 4, 5
Hence Range of f(x) = {4P0, 3P1, 2P2}
Range of f(x) = {1, 3, 2}
Let f and g be differentiable functions satisfying g′(a) = 2, g(a) = b and fog = I (identity function). Then f ′(b) is equal to
1/2
2
2/3
2/3
Let S = {t ∈ R: f(x) = |x-π|.(e|x| - 1) sin |x| is not differentiable at t}. Then the set S is equal to
{0,π}
{0}
{π}
Let S = { x ∈ R : x ≥ 0 and Then S:
Contains exactly four elements
Is an empty set
Contains exactly one element
Contains exactly two elements
On the set R of real numbers we define xPy if and only if . Then, the relation P is
reflexive but not symmetric
symmetric but not reflexive
transitive but not reflexive
reflexive and symmetric but not transitive
On R, the relation p be defined by 'xy holds if and only if x- y is zero or irrational'. Then,
s reflexive and transitive but not symmetric
s reflexive and symmetric but not transitive
s symmetric and transitive but not reflexive
is equivalence relation
Mean of n observations x1, x2, ..., xn, is . If an observation , is replaced by xq', then the new mean is