Question

If f(x)=ln x and g(x)=e^x+1 find f(g(2))-g(f(e)) please help!!

Answer 1

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)