FunctionMedium
Question
If f(x) = cos (log x ), then f(x).f(y) 
has the value
has the value Options
A.-1
B.
C.-2
D.None of these
Solution
Given, f (x) = cos (log x)
∴ f(x).f(y)
= cos (log x ). cos (log y )-
[cos(log x - log y) + cos (log x + log y)]
= cos (log x ). cos (log y ) - [(2 cos (log x). cos (log y)]
= cos (log x ). cos (log y ) - cos (log y) - cos (log x). cos (log y) = 0
∴ f(x).f(y)
= cos (log x ). cos (log y )-
[cos(log x - log y) + cos (log x + log y)]= cos (log x ). cos (log y ) -
[(2 cos (log x). cos (log y)] = cos (log x ). cos (log y ) - cos (log y) - cos (log x). cos (log y) = 0
Create a free account to view solution
View Solution FreeMore Function Questions
The function f(x) = x2 − |x| is -...If f(x) is an odd periodic function with period 2, then f (4) equals to -...If the domain of the function$$f(x) = \log_{\left( 10x^{2} - 17x + 7 \right)}\left( 18x^{2} - 11x + 1 \right)$$is $( - \...The functionf(x) = {2(t - 1) (t - 2)3 + 3(t - 1)2 (t - 2)2}dt attains its maximum at x is equal to :-...If f(x) = (ax − c)/(cx − a) = y, then f(y) equals-...