Question

CAN SOMEONE PLZ PLZ HELP ME? :)

6.The Martians ask you to explain one last thing, Ultimate Math Ambassador. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number. You will use the inverse function that you created in problem number 5 for g(x).

ok the functions I have are
f(x)=2+10x
and
the inverse, im not sure which one im supposed to use, I have
y=2+10x
and
f^-1(x)=x-2/10

I have no idea how to set this one up cuz Idk which one im supposed to use

Answer 1

the inverse of \(f(x)=10x+2\) is what you said, \(f^{-1}(x)=\frac{x-2}{10}\)

Answer 2

yes I know, I have to use both the original function and the inverse, I don't know which version of the inverse to use

Answer 3

if you compose them you get \(x\) because
\[f(f^{-1}(x))=f(\frac{x-2}{10})=10\times \frac{x-2}{10}+2=x-2+2=x\]

Answer 4

also you get \(x\) if you compose them as
\[f^{-1}(f(x))=f^{-1}(10x+2)=\frac{10x+2-2}{10}=x\]

Answer 5

wait so are both of those the two versions I needed?
f(g(x)) and g(f(x))

Answer 6

i think so yes

Answer 7

well then! lol thanks :)

Answer 8

" explain whether \(f(g(x))\) and \(g(f(x))\) will always result in the same number"

Answer 9

yea, now I have to plug in a number for x to prove that

Answer 10

no not at all
if you prove it for \(x\) then it must be true for any number
that is what "\(x\)" represents, "any number"

Answer 11

even tho it says to assign any number to/for x?

Answer 12

ok you can use a number as an example then

Answer 13

lol im just checking cuz I don't wanna get it marked wrong

Answer 14

oh wait I have to explain how they are equal, so how would I write the equations using words?

Answer 15

i will let you use the words yourself
i would say something like "f says to multiply by 10, add 2" the inverse does the opposite in the opposite order, subtract 2, divide by 10. so you get back to where you started frmo when you do one and then the other"

Answer 16

coolio, ill have to switch the wording around yea, thanks for ur help! :)