Question

已知f(1+x除以x)=1+x的平方除以x的平方+1除以x,求f(x)

Answer 1

f[(1+x)/x]=(1+x²)/x²+1/x

即:

f(1+1/x)

=(x²+x+1)/x²

=1+1/x+1/x²

=(1+1/x)²-1/x

=(1+1/x)²-(1+1/x)+1

所以,f(x)=x²-x+1