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.
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