Question

The Martians ask you to explain one last thing, Ultimate Math Ambassador. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number. You will use the inverse function that you created in problem number 5 for g(x). ...... I'm lost

Answer 1

what are f(x) and g(x) ?

Answer 2

you have to creat two functions g(x) f(x) to prove that
f(g(x)) not always = g(f(x))
try using
f(x)=x^2
g(x)=3x

Answer 3

Haha I'm so lost still after the f(x) and the g(x)

Answer 4

assuming
f(x)=x^2
g(x)=3x
f(g(x))=9x^2
g(f(x))=3x^2
using contradiction
assume
f(g(x))=g(f(x))
9x^2=3x^2
9=3 wich is a contradiction
Hint do the prove using x= 5
f(g(5))=9*5^2=255
g(f(5))=3*5^2=75
you can note that
255 !=75
We conclude that f(g(5)) do not = g(f(5))
its congruent to f(g(x)) do not = g(f(x))