[f(x)]＾2-[f(y)]＾2=f(x+y)f(x-y) 求f(x)

H2L

对任意实数x,y均有\(\left[ f\left( x\right)\right]^2-\left[ f\left( y\right)\right]^2=f\left( x+y\right)f\left( x-y\right)\)成立，求满足条件的f(x)

Treenewbee

目测 \[f(x)=0\  or\  f(x)=kx\]

Treenewbee

目测 \[f(x)=0\  or\  f(x)=kx\]

H2L

Treenewbee 发表于 2024-4-9 20:06
目测 \[f(x)=0\  or\  f(x)=kx\]

是的  \(f\left( x\right)=k\sin x和f\left( x\right)=k\sinh x\) 也成立  不知道有无其他解