Question

Please help me it's my last question!

the Martians ask you to explain one last thing, Ultimate Math ambassador. they ask you to create a new function a new function .h(x).Then assign any number to x. Using complete sentences explain weather 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 number 2.

I created f(x)=10x+6

Please help me whoever ASAP ...

Answer 1

well i guess the only way you know is to try

Answer 2

let's just pick something random like h(x)= 3x-5 and try if it's the same or not

Answer 3

I'm extremely confused with this question I don't even know how to start it

Answer 4

ah right

Answer 5

well, you know that f(x)=10x+6 is a function with x as variable and the function name is f, right?

Answer 6

Could you please help lol I'm desperate I just need this last question and I'm done .

Answer 7

Yes

Answer 8

so if i were to say for example f(4) (the function named f with 4 as 'argument') that would result in 10*4+6, in other words f(4) = 46

Answer 9

now, let's step it up a notch

Answer 10

Okay

Answer 11

what if, instead of providing an integer as argument for x, we choose another function named h as the argument. In other words, wherever there used to be an 'x' in the function named 'f', we insert the conplete function named h.

Answer 12

Okay !(:

Answer 13

Ok

Answer 14

so, in the function f we already have, we insert the function h like this:
let's say h(x)= 3x-5

then
f(h(x))= 10\(\color{red}{( 3x-5)}\)+6

Answer 15

see how only the x gets substituted with the function of h, including the x that was in h

Answer 16

Okay

Answer 17

Yes

Answer 18

of course you can now remove the brackets and make it simpler, so you oculd work it out to 30x-50+6 = 30x-44 in the simplest form

so in other words f(h(x)) = 30x-44

Answer 19

now let's do it the other way around, let's use the function of f as an argument to h, so

h(f(x)) =

could you try to do that?

Answer 20

Would that be the last step I do or would I get going ??

Answer 21

that's the simplest way you can write it down

Answer 22

So that's it I wouldn't have to add anymore to the problem???

Answer 23

you don't need to simplify it, but it's good practice to simplify things to have a clearer view, otherwise things can get messsy

Answer 24

Your seriously a life savior

Answer 25

oh no, you still need to do the other side to compare them

Answer 26

we only have 1 part of the problem now, we need to compare it to see if they are the same

Answer 27

Ahh :( okay ah I really thought we were done ha!

Answer 28

could you work out h(f(x)) the same way i did f(h(x)) and see if both of them work out to the same or not? because that was the question we need to ultimately solve

Answer 29

t's also a good tst to see if you understood it all, practicing makes you understand it even better

Answer 30

No I still need your help if you don't mind?

Answer 31

that's ok

Answer 32

what you basically do is you take the function h(x) (which i defined as 10x+6) and for each 'x' you replace it with (10x+6) (which is the f(x) you chose)

Answer 33

Okay so what would I be doing next?

Answer 34

Okay

Answer 35

then, after you have done that, you simplify it, and see if it's the same as the one i made. If it's not the same than the answer to your question is no. If they are the same than the answer is yes.

Answer 36

first you take the function h(x) = 3x-5

Answer 37

than you remove the x, and instead of the x you write (10x+6)

Answer 38

that is h(f(x)) (you take the function named f as an argument for the function named h, while x is the argument to function f) I understand it can be a bit confusing, but it's essentially the same as using a number as an argment, it's just a longer string instead of a number.

Answer 39

Okay and then ?

Answer 40

Is that it or is there more to it?

Answer 41

then you get h(f(x)) = 3(10x+6)-5

Answer 42

than you compare 3(10x+6)-5 or simplified 30x+13 to 30x-44

as you can see it's not the same.

so in conclusion f(h(x)) is not the same as h(f(x))

Answer 43

Okay(:

Answer 44

you might want to read this a few more times until you understand it completely

Answer 45

it's a bit difficult the first time but once you understand it it can be very handy

Answer 46

Okay(:!

Answer 47

Is that it?

Answer 48

Thank you soo much !!!!