Answer:
ln (e^2 + 1) - (e+ 1)
Step-by-step explanation:
Given f(x) = ln and g(x) = e^x + 1 to get f(g(2))-g(f(e)), we need to first find the composite function f(g(x)) and g(f(x)).
For f(g(x));
f(g(x)) = f(e^x + 1)
substitute x for e^x + 1 in f(x)
f(g(x)) = ln (e^x + 1)
f(g(2)) = ln (e^2 + 1)
For g(f(x));
g(f(x)) = g(ln x)
substitute x for ln x in g(x)
g(f(x)) = e^lnx + 1
g(f(x)) = x+1
g(f(e)) = e+1
f(g(2))-g(f(e)) = ln (e^2 + 1) - (e+ 1)
