Let f(x)=ex−e−x2  and if f(g(x))=x  then g(e1002−12e501)=___

y=ex−e−x2⇒e2x−2yex−1=0 put ex=t ⇒t2−2yt−1=0t=y±y2+1x=log(y+y2+1)f−1(x)=log(x+x2+1) ∴g(e1002−12e501)=log(e1002−12e501+e1002+12e501) =loge501=501