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Ques1) Let f(x+y) + f(x-y) = 2 f(x) f(y), for all x,y belonging to R and f(0) = k ; then (a) f is even if k=1 (b) f is odd if k=0 (c) f is always odd (d) f is neither odd nor even for any value of k

 

Ques1) Let f(x+y) + f(x-y) = 2 f(x) f(y), for all x,y belonging to R and f(0) = k ; then


(a) f is even if k=1


(b) f is odd if k=0


(c) f is always odd


(d) f is neither odd nor even for any value of k


 


Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear Sanchit

f(x+y) + f(x-y) = 2 f(x) f(y), for all x,y belonging to R and f(0) = k

put x=0

f(y) + f(-y) = 2 f(0) f(y)

f(y) + f(-y) = 2 k f(y)

f(-y)=-(1-2k)f(y)

now for k=0

f(-y)=-f(y)

so f(y) is odd

and for k=1

f(-y)=f(y)

f(y) is even

so option a and b is correct


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Badiuddin

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