Question

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

Answer 1

compose them and see that you get the identity back

Answer 2

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

Answer 3

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

Answer 4

Got it, Thank you!

Answer 5

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