Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x

Answer 1

f(x)=9x+3 g(x)=x-3/9

Answer 2

please help!!

Answer 3

when you calculate f(g(x)) : think this way:
g(x) is the new substitution of x.
So replace x with the value you have for g(x) in f(x)
You will get f(g(x)) this way

Answer 4

Similarly calculate g(f(x))

Answer 5

so f(g(x)) will equal 9(x-3)+3? What do i have to do after that?

Answer 6

Remember what function notation means: it means that you "plug in" whatever is in the ( ) for the variable in the definition of the function, right?

\(\Large g(x)=(x-3)/9\\
\text{then } \Large g(6)=(6-3)/9\\
\text{and } \Large g(a)=(a-3)/9\\
\text{and } \Large g(r+1)=[(r+1)-3]/9\)

So to find g(f(x)) you'll just want to plop f(x) into g(x) in place of the variable x, and simplify the resulting expression:

\(\Large g(f(x))=g(9x+3)=[(9x+3)-3]/9\)

Simplify that, and you'll see that you get x.

Now do the same thing, inthe other direction, that is, find f(g(x)). You should also get x (but show each step!)

Answer 7

What you said above is not correct for f(g(x)).

Answer 8

\(\Large g(x)=(x-3)/9\\
\text{and } \Large f(x)=9x+3\\\)

then \[\Large f(g(x))=f(\frac{ x-3 }{ 9 } ) = 9(\frac{ x-3 }{ 9 } )+3\]

Answer 9

how would you simplify it after your plugged it in? I just need to understand how it would be done for f(x). So once you get that f(g(x)=9(x-3/9) + 3 what do i have to do after that, if you dont mind.

Answer 10

Just use some basic algebra :)

\(\Large \cancel9(\dfrac{ x-3 }{ \cancel 9 } )+3\)

Now what do you get?

Answer 11

ahhh! you will then be left with x-3+3 and the 3s will be negated leaving the answer to be x right??

Answer 12

Remember, if you know for certain that f and g are inverses (e.g., the problem tells you THAT THEY ARE, not asks you to DETERMINE WHETHER THEY ARE) then when you take the two compositions:

f(g(x)) and g(f(x))

everything should just fallll right into place so that each simplifies to x. That's what it means for them to be inverses. :)

Answer 13

Exactly right! :)

Answer 14

Wow! Thank you so so much!! This really clears up everything! :) Thank you again for your help! :)

Answer 15

you're very welcome. :) happy to help.

And welcome to Open Study!! :)