Question

F(x)=ln(x) g(x)=e^x+1. F(g(x)) must then be ln(e^x+1) right? Can you simplify this?

Answer 1

is that e^(x+1) ?

Answer 2

e^x and ln(x) are inverse functions so:
\[\ln(e^x) = x\]

Answer 3

yes you are right

Answer 4

No, g(x) is just e^x+1, as if it was 1+e^x without any parenthesis

Answer 5

\[f(g(x))= \ln(e ^{x}+1)\]

Answer 6

let me know if u need furthur help :)

Answer 7

oh btw you cant simplify further

Answer 8

or maybe write Near x=0, I suppose you could expand e^x,

Answer 9

because ln(1) = 0 and also ln(e^x) is also 0 because they are inverse pairs

Answer 10

So that makes it x+1 in the end. But the reverse, g(f(x)) = e^ln(x)+1 will also become x+1? Right?

Answer 11

Ah, ok :)