Question

For the functions f(x)=x^5 and g(x)=x+4, find the following:

f(g(1)): Did I do this one right? f(1+4)=f(5)=5^5=3,125

g(f(1)): What about this one?
g(1^5)=g(1)=1+4=5

f(g(x)): f(x+4)=(x+4)^5
did I start that right? :/ and if so, is that as simplified as it gets?

g(f(x)): g(x^5)=(x^5) + 4
is that right? and is that as simplified as it can get?

f(t)g(t): this one i'm a bit confused on :/ would it just be (x^5)(x+4)=x^6+4x^5 ?

Thank you!!! :)

Answer 1

g(1)=1+4=5
f(5)=5^5=3125

Answer 2

f(t)g(t)=(t^5)(t+4)=t^6+4t^5 not x

Answer 3

(x^5) + 4 you can drop the brackets, that's it

(x+4)^5 doesn't get any more simplified unless you like doing really boring unnecessary work.

Answer 4

f(1)=1^5=1
g(1)=1+4=5

g(x)=x+4
f(x+4)=(x+4)^5 = x^5+20 x^4+160 x^3+640 x^2+1280 x+1024

Answer 5

^yeah there is your unnecessary work. Don't do that.

Answer 6

oh right haha forgot...

wait so would these be correct then?

f(g(1))=3,125

g(f(1))=5

f(g(x))=(x+4)^5

g(f(x))= x^5+4

f(t)g(t)=t^6+4t^5

?? are those the final correct answers then? :)

Answer 7

haha okay @agent0smith :) i won't :)

Answer 8

thanks!!! :)