Set, Relation and FunctionMedium
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 f(x) be a differentiable function on interval (0, ∞) such that f(1) = and then f(2) has value equal to...Let a relation ′R′ is define on ′Z′ set of integers such that a R b ⇒ a is divisible by b ...Let f(x) = , a > 0, x ≥ 0, then which of the following is/are correct ?...If A denotes the area between the curve 2{y} = [x] + 1 for 0 ≤ y 2 - x ≤ 0, then A is less than or equal to ...Let f(x) be a function satisfying f′(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x...