Question

Please help: The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to 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. You will use the function f(x) that you created in problem number 2.

Answer 1

The other function:f(x) = 7x + 2

Answer 2

H(x) = 2x - 4

Answer 3

H(5) = 2(5) – 4
H(5) = 10 – 4
H(5) = 6

Answer 4

@Idealist10

Answer 5

was this right?
H(5) = 2(5) – 4
H(5) = 10 – 4
H(5) = 6
7(2(5) – 4) – 2
7(6) – 2
42 – 2 = 40

Answer 6

@asib1214 @Ashy98 @Whitemonsterbunny17 @RaphaelFilgueiras @Elsa213 @ganeshie8 @Hero

Answer 7

Right now I don't have time, Please wait...

Answer 8

H(5)=6 and f(5)=7*5+2=37.

Answer 9

I do not understand.

Answer 10

f(h(x))=7(2x-4)+2
h(f(x))=2(7x+2)-4
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for example, if you plug in 5,
f(h(5))=7(2*5-4)+2=7(10-4)+2=7*6+2=44
h(f(5))=2(7*5+2)-4=2(35+2)-4=2*37-4=70
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f(h(x)) and h(f(x)) will not result in the same number.

Answer 11

Oh i see. It wouldn't result with the same number because the base formula is too different from each other?

Answer 12

isn't h(x)=f-1(x)?

Answer 13

Wouldn't that be an inverse equation then?

Answer 14

h(x)=x^1/3, and f(x)=x^3

Answer 15

the inverse has that property, but it's the unique solution?

Answer 16

I have no idea. I have submitted it already so i will wait and see.

Answer 17

@RaphaelFilgueiras , but the functions aren't inverses.