Question

explain whether f(h(x)) and h(f(x)) will always result in the same number pleaseeeeeeeeee? I really need help and ill give out medals and become fans

Answer 1

They ask you to create a new function, h(x). Then assign any number to x

Answer 2

Just do an example. f(x) = x + 1
Let h(x) = x^2
Create both composite functions, see what you get.

Answer 3

Hmm, that doesn't really make sense. o.o Create any function?

Answer 4

here ill get the full question

Answer 5

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 6

Ahh, ok. So, what was the function, f(x) that you created in problem 2?

Answer 7

f(x) = 5x+2

Answer 8

Ok, cool. Now, let's create use some simple function for h(x). Like h(x) = x^2

Answer 9

ok

Answer 10

Do you know what composite functions are? Do you understand what f(h(x)) and h(f(x)) mean?

Answer 11

i understood them when they were asked in a question for, but not when i have to create them myself

Answer 12

Oh, it's easier when you have to create them yourself. XD It makes the question simpler.
So, in that case, can you find f(h(x))?

Answer 13

so, f is 5 + 2

Answer 14

then what?

Answer 15

5x*

Answer 16

f(x) = 5x + 2
And for f(h(x)), we want to plug in h(x) into each x of f(x).
h(x) = x^2
f(h(x)) = 5(x^2) + 2

Answer 17

That simple. Do the similar thing to h(f(x)). And you'll see if they're similar or not.

Answer 18

but what is x?

Answer 19

i dont understand how to plug in

Answer 20

I think they were saying just to use 'x' as a variable for a number.

Answer 21

h(x) = x^2
For h(f(x)), you're plugging in f(x) into the 'x' in h(x).

Answer 22

so i plug in 5x +2 ?

Answer 23

Yes, into the x in x^2.

Answer 24

how would that work
im so confused sorry

Answer 25

oh ok
so 5^2 + 2?

Answer 26

h(f(x)) = (5x + 2)^2
I just plugged the entire function of f(x) into x. And the entire thing is squared.

Answer 27

but how do you solve that?

Answer 28

You can expand it out. We're just making functions, not evaluating them. They ask you to determine whether f(h(x)) and h(f(x)) will give you the same result.

Answer 29

so you don't need to solve it?

Answer 30

so for f(h(x)) it would be 5x+2(^2) ???

Answer 31

Nooo.f(h(x)), we plugged h(x) into the x in f(x).