A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = x9/x+5
and g(x) = 5x9/x1
PLEASE HELP I GIVE MEDALS
anonymous
 3 years ago
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = x9/x+5 and g(x) = 5x9/x1 PLEASE HELP I GIVE MEDALS

This Question is Open

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So, remember when you find the inverse of a function you turn the "f(x)" in y, then set that equal to the function, then switch the place of y and x, then solve for y. (get y by itself) Thats how you would get g(x) (assuming we aren't given g(x) like in your problem). Thus, to check if the given functions are inverses of each other, find the composite of the f(x) "f of x" and g(x) "g of x", which is the same as [f o g], f(g(x)) read "f of (g of x)" (remember g(x) is read as "g of x".) Now, \[f(x)=\frac{ x9 }{ x+5 }\] and \[g(x)=\frac{ 5x+9 }{ x1 }\] \[f(g(x))\] NOTICE: \[g(x)=\frac{ 5x+9 }{ x1 }\] So, just replace it. \[f(\frac{ 5x+9 }{ x1 })= \frac{ x9 }{ x+5 }\] (remember: if f(x)=x+3, find what x=2 is?... f(2)=2+3 f(2)=5 ) Do the with the eq \[f(\frac{ 5x+9 }{ x+1 })=\frac{(\frac{ 5x9 }{ x+1 })9 }{ (\frac{ 5x9 }{ x+1 })+5 }\] Then, solve, if f(g(x))=x then, they are inverse. Though, it would be a lot easier to just find the inverse of f(x), and compare it to g(x)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.