Set, Relation and FunctionHard
Question
Which of the following statement(s) is/are correct about continuous functions y = f(x) & y = g(x) ?
Options
A.h(x) = max {f(x) - 2g(x), 
} is continuous.
} is continuous.B.If f(x) & g(x) are real polynomials of degree 5 and 7 respectively, then the equation f(x).g(x) = 0 has atmost 10 imaginary roots.
C.
f(x) = 0 ⇒ f(x) . g(x) = 0
f(x) = 0 ⇒ f(x) . g(x) = 0D.(f(x) + g(x)) = f(x) + g(x)
(f(x) + g(x)) = f(x) + g(x)Solution
(A) max(f(x),g(x)) is always continuous if f(x) & g(x) are continuous
(B) f(x) & g(x) has atleast one real root
(C)
f(x). g(x) = 0
∵ g(x) is continuous at x = 0
(D) true
∵ f(x) & g(x) are continuous at x = 0.
(B) f(x) & g(x) has atleast one real root
(C)
f(x). g(x) = 0∵ g(x) is continuous at x = 0
(D) true
∵ f(x) & g(x) are continuous at x = 0.
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let ƒ, g : [−1, 2] → be continuous function which are twice differentiable on the interval (−1, 2...Let p(x) be a function defined on R such that p′(x) = p′(1 - x), for all x ∈ [0, 1], p(0) = 1 and p(1)...If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by ′x is greater than y′. The ran...Let X = {1,2,3,4,5,6} be an universal set. Sets A,B,C in the universal set X be defined by A = {1,2,3},B = {2,4,5} & C =...The number of relations, defined on the set $\{ a,b,c,d\}$, which are both reflexive and symmetric, is equal to:...