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let f(x/2+y/2)=f(x)/2+f(y)/2 , x,y belongs to real no.
f ' (0) exists and is equal to -1 and f(0)=1 , then find the value of f(2)
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9 Answers
1put y=0;
f(x/2)=f(x)/2 + 1/2.
f(x)=f(2x)/2 + 1/2.
f'(x)=lim h→0 (f(2x)/2+f(2h)/2-f(x))/h = lim h→0 (f(h)-1/2 - 1/2)/h
=f'(0)=-1.
f(x)=-x+c
f(0)=0 so c=1.
f(x)=1-x...
1ok , may be i m confused but where it is given that f'(x)=-1
