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).

Question

ddcamp · Answer

From problem 5, what are f(x) and g(x)?

anonymous · Answer

(x-10)/2=g(x)

anonymous · Answer

F(x)=2x+10

anonymous · Answer

do i plug in my value for g(x) into my f(x)?

anonymous · Answer

g(x)= (x-10)  
	        2
g(20)= (20-10)
		2
g(20)= 10/2
g(20)=5
 i think i did that correctly..

ddcamp · Answer

Yes, I think that would work. 
The other thing you could do is replace each x in f(x) with g(x):
$$2x+10 \rightarrow 2(\frac{ x-10 }{ 2 }) + 10$$

ddcamp · Answer

Just to show that f(g(x)) = x and g(f(x)) = x in all situations.

anonymous · Answer

so do i plug in my x value (20) into that equation?

anonymous · Answer

never mind thank you :)