Question

(1)已知f(1-x)=2x^2-x+1,求f(x) (2)已知f( x-1/x)=x^2+1/ x^2，求f(x)

(3)已知f(x)是二次函数，且满足f(0)=1,f(x+1)=f(x)+2x，求f(x)
拜托了！

Answer 1

1-x=a
x=1-a
f(x)=2(1-x)²-1+x+1
=2x²-3x+2
f(x-1/x)=x²+1/x²
=x²-2+1/x²+2
=(x-1/x)²+2
f(x)=x²+2
f(x+1)=f(x)+2x
f(x)=f(x-1)+2(x-1)
.......
f(2)=f(1)+2
上面所有式子相加
f(x+1)=f(1)+2+4+6+8+...+2(x-1)+2x
f(x)=1+2+4+6+8+...+2(x-1)
=1+2(1+2+3+...+x-1)
=1+x(x-1)
=x²-x+1

Answer 2

解答过程如图