f(x+x/1)=x2+x2/1,求f(x+1)

Question

f(x+x/1)=x2+x2/1,求f(x+1)

Answer 1

解：
f(x+ 1/x)=x²+ 1/x
=x²+2 +1/x -2
=(x+ 1/x)² -2
将x+ 1/x换成x+1
f(x+1)=(x+1)²-2=x²+2x+1-2=x²+2x-1
f(x+1)=x²+2x-1