Question

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

My function is f(x) 4x +6
The inverse of it is f-1(x) = x - 6 /4

Answer 2

@waterineyes

Answer 3

h(x) can be anything..

So, say let us take as h(x) = 2x + 3

Answer 4

Can you find f(h(x))??

Answer 5

oops sorry was making a sandwich

Answer 6

so could you use 3 for x?

Answer 7

f(3)2x + 3
f(3)6 + 3
f(3)9

What now..?

Answer 8

@waterineyes

Answer 9

Sorry, I gotta go now... :)

@campbell_st when you are free, please look at this question.. :)

Answer 10

well looking at the 2 functions

the domain of f(x) will become the range of the inverse f^(-1)

and the range of f(x) will become the domain of the inverse f^(-1)

that seems to be the idea here...

so if you put a value from the domain of f(x) say 1 then f(x) = 10

then substituting that into the inverse will give a solution of 1.

hope it makes sense

Answer 11

so it that supposed to be relating f(h(x)) and h(f(x)) together?

also, i dont really get what i'm using the function from #2 for? proving the result will be the same?

Answer 12

ok... so do it this way

f(x) = 2x

h(x) = x + 2

h(f(x) = (2x) + 2 = 2x + 2

now the other way

f(h(x)) = 2(x + 2) = 2x + 4

are they the same things.... h(f(x) and f(h(x))...?

Answer 13

so in the 1st case

h(f(x)) replace x in h(x) with 2x from f(x)

then reverse it...

do you get the same equation...

Answer 14

well you ended up with 2x + 2 and 2x +4 so no

Answer 15

so that's it i guess?