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.

the function that I am using is f(x)=4x+2

Answer 1

depending on whether or not h(x) is the inverse of f(x), your answer would vary

Answer 2

that's all it gives me

Answer 3

have you covered inverse functions yet?

Answer 4

yes I have. but I don't understand this question

Answer 5

as bibby said....
" f(h(x)) and h(f(x)) will always result in the same number" <---
will only occur IF h(x) is the inverse of f(x)

so in order to f( h(x) ) to result in the same number as the other way around
h(x) has to be the inverse

now, if h(x) is NOT the inverse of f(x).... the values will vary as bibby said

I think you're being asked to produce an h(x)
doesn't have to be the inverse of f(x)
and then explain if it does or it does not result in the same values as asked

Answer 6

okay so the other function I madu up is h(x)=3x+2, so now with the two functions I made up wat do I do

Answer 7

"\(\bf {\color{blue}{ \text{Then assign any number to x.}}}\) Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number."

Answer 8

okay so h(x)=4. now I do 3(4)+2 which equals 14. correct? then I explain that yes I got the same answer for both

Answer 9

hmmm

well... if you set x = 4

then h(x) = 3(4)+2 = 14 yes

but you're asked to do \(\bf f(\quad h(x)\quad )\iff (f\circ h)(x)\qquad h(\quad f(x)\quad )\iff (h\circ f)(x)\)

Answer 10

\(\bf {\color{blue}{ f(x)}}=4x+2\qquad {\color{brown}{ h(x)}}=3x+2
\\ \quad \\
f(\quad {\color{brown}{ h(x)}}\quad )=4{\color{brown}{ h(x)}}+2\qquad h(\quad {\color{blue}{ f(x)}}\quad )=3{\color{blue}{ f(x)}}+2\)