Create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. Equations: f(x)=2x+10 h(x)=3x+4 I chose x to equal 6 but how do I explain how the numbers won't repeat?

Question

Create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number.  Equations: f(x)=2x+10   h(x)=3x+4  I chose x to equal 6 but how do I explain how the numbers won't repeat?

anonymous · Answer

f( h(x) ) is f(x), where x=h(x).  2(3x+4)+10

h( f(x)) is h(x) where x is f(x)  3(2x+10)+4

anonymous · Answer

2(3x+4)+10 = 6x+8+10 = 6x+18

3(2x+10)+4  = 6x+30+4 = 6x+34

anonymous · Answer

Using x=6 for both we get:

6(6)+18 = 54
6(6)+34 = 70  They will not result in the same number because the number following the 6x in both equations are different

anonymous · Answer

@Mchilds15

mchilds15 · Answer

Oh thank you so much! I've been trying to figure this thing out for awhile... @larryboxaplenty