Question

Find and simplify expressions for f(g(x)) and g(f(x)) where f(x)=e^(x)+3 and g(x)=ln(x-3). Also find the inverses. You should get for answers. Help please!

Answer 1

f(g(x)) = e^(ln(x-3)) + 3 = x - 3 + 3 = x

g(f(x)) = ln(e^(x) + 3 - 3) = ln(e^x) = x

hence they are inverses of each other

Answer 2

I'm sorry for the mix up but it's actually:
f(x)=e^(x+3) and g(x)=ln(x-3)
1. f(g(x))=
2. g(f(x))=
3. Inverse f(x)=
4. Inverse g(x)=

Thank you so much