Question

已知函数f(x)=a^(x+b)(a>0,a≠1),满足f(x+y)=f(x)*f(y),且f(3)=8,求f(x)的解析式

Answer 1

f(x+y)=a^(x+y+b);
f(x)*f(y)=a^(x+b)*a^(y+b)=a^(x+y+2b);
则,2b=b,b=0;
s所以f（x）=a^(x);
又有 f（3）=8;得
a^(3)=8;
a=2;
所以f(x)=2^(x);