A.If we know that e^(f(x))+f(x)=x+lnx,x>0 prove that f(x)=lnx
B.If we know that f,g:R->R and f^2(x)+g^2(x)=x^2,xER,prove that f,g are continuous at x=0
C.If we know that f:R->R and f^5(x)+f(x)=x,xER prove that f is continuous at x=0
+37146 Just substitute lnx in where f(x) is to see this:
e^(lnx) + lnx =
( e^ln x is by definition, just 'x' )
x + lnx
