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

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