Suppose that we have equation: $f(x)=\frac{2^x+1}{2^x-1}$
There is question if this function even or odd? I know definitions of even and odd functions, namely even is if $f(-x)=f(x)$ and odd is if $f(-x)=-f(x)$ and when I put $-$ sign in function, found that this is neither even nor odd function, because $2^{-x}\ne-1 \times 2^x$, but my book says that it is even, so am I wrong? Please help me to clarify book is correct or me? Thanks