Question

find a function f(y) such that f(1+lnx)=x for all x>0

Answer 1

f(y)=e^(y-1)
then y=(1+lnx) and f(y)=f(1+lnx)=e^((1+lnx)-1)=e^lnx=x
for all x>0

Answer 2

can you explain it? but thank you

Answer 3

I'll try to explain my reasoning. First I set 1+ln(x)=x, then I subtract the 1 from both side to form ln(x)=x-1. Next I raise both side as a power of e, obtaining e^ln(x)=e^(x-1). This simplifies to x=e^(x-1). All we need now is to change the variable x to y.

Answer 4

that makes sense thank you