A function f is defined on the set of all real numbers except 0 and takes all real values except 1. It is also known that\color{white}\ . \ \color{black}\ f(xy)=f(x)f(-y)-f(x)+f(y)for any x,y=0 and that\color{white}\ . \ \color{black}\ f(f(x))=\frac{1}{f(\frac{1}{x})}for any x∈{0,1}. Determine all such functions f. functionalgebra proposedalgebra