Question

f（e的x+1次方）=e的2x次方+e的x次方+1,求f（x）=

Answer 1

f(e^(x+1)）=e^(2x)+e^x+1

• y=x+1

f(e^y）=e^(2(y-1))+e^(y-1)+1

= (1/e^2)(e^y)^2 + (1/e)e^y +1

• x=e^y

f(x) =(1/e^2)x^2 + (1/e)x +1

Answer 2

f(e^(x+1))=e^(2x)+e^(x)+1
let
y = e^(x+1)
f(x)=e^(2x)+e^(x)+1
= e^(2x+2)/e^2 + e^(x+1)/e +1
f(y) = y^2/e^2 + y/e + 1
f(x)=x^2/e^2 + x/e + 1