Question

For the function f(x)=5e^x and g(x)=x^5, find the following:

(a) f(g(1))=
(b) g(f(1))=
(c) f(g(x))=
(d) g(f(x))=
(e) f(t)g(t)=

Answer 1

simple substitution and manipulation

I will do b) and c)

b) f(1) = 5e^1 = 5e
then g(f(1)) = g(5e)
= (5e)^5 or 3125e^5

c)
f(g(x))
= f(x^5)
= 5e^(x^5)

You do the others, show me your work and I will check it.

Answer 2

a.) g(1)= 1^5= 1
f(g(1))=5e^1=
5e?

d.) g(f(x))= g(5e^x)
= (5e^x)^5?

e.) I'm really guessing on this last one because I'm not sure but I'll try it anyway
((5e)^t)(t^5)?