A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Let f(x)=10x10. Find the value of (f o f^1)(10)
anonymous
 one year ago
Let f(x)=10x10. Find the value of (f o f^1)(10)

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x) is a onetoone function (it's a line) so (f o f^1)(10) = 10

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0basically, inverses "undo" each other, so you end up with the same value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok and so i plug the 10 into the original equation or would that be the answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope.\[f(f^{1}(10)) = x\]\[10=x\] That's basically what is going on. \[f(10)=10x10 = 110 \ne 10 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, forgot to substitute by 10 in for x. \(f(10)=10(10)10 = 110\)*

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.3\[f(x) = 10x10\\[3ex] x=10\Big(f^{1}(x)\Big)10\\ x+10 = 10(f^{1}(x))\\ f^{1}(x)=\frac {x+10}{10}\\[3ex]f\circ f^{1}(x)=f\Big(\frac {x+10}{10}\Big)\\ \qquad\qquad\quad = 10\Big(\frac {x+10}{10}\Big)10\\ \qquad\qquad\quad = x+1010\\ \qquad\qquad\quad =x\\[2ex] f\circ f^{1}(10) =10\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f \circ f^{1}(x)=x\] A function and it's inverse cancel each other out, leaving you with the independent variable x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I like the way @UnkleRhaukus proved it and then found the value.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mmhm, it has a beauty of it's own
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.