f(x) ln x+2; g(x)= e^x-2 How to show how f and g are inverses of each other?

Question

anonymous · Answer

compose them and see that you get the identity back

anonymous · Answer

$$f\circ g(x)=f(g(x))=f(e^{x-2})=\ln(e^{x-2})+2=x-2+2=x$$ in one direction

anonymous · Answer

i hope that is clear, i wrote 5 equal signs
first one is definition of the circle notations
second one is replacing the generic $f$ by the specific one you have
third is evaluating $f$ at $e^{x-2}$
fourth is because log and exp are inverse functions '
fifth is arithmetic

anonymous · Answer

Got it, Thank you!

anonymous · Answer

yw
i made a typo in my response however, should have been 
"second one is replacing he generic $g$ by the specific one "