Let g(x)  be a polynomial of degree one and f(x) be defined by  f(x)=g(x),           x≤0|x|sinx,         x>0  If f(x) is continuous satisfying f'(1)=f(−1),  then g(x) is

f(0+)=limx→0+|x|sinx=1 f(0−)=g(0)=1 Let g(x)=ax+b For x>0,  f'(x)=esinxln(|x|)[cosxln(|x|)+sinxx] f'(x)=1[0+sin1]=sin1 f(−1)=−a+1⇒a=1−sin1 g(x)=(1−sin1)x+1