A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Let f(x)=3+×^2+tan((pi)(x)/2), where 1 <×<1
A) find f^1 (3)
B) find f (f^1 (5))
anonymous
 one year ago
Let f(x)=3+×^2+tan((pi)(x)/2), where 1 <×<1 A) find f^1 (3) B) find f (f^1 (5))

This Question is Open

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know that when you inverse a function you switch the x and the y values. But I don't know what to do with the y value instead of x in tangent.

rational
 one year ago
Best ResponseYou've already chosen the best response.3for part A, you need to solve : \[3 = 3+x^2+\tan(\pi x/2)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't the x value be 3?

rational
 one year ago
Best ResponseYou've already chosen the best response.3nope, as the name says, \(f^{1}(3)\) is the value of \(x\) that makes the function \(f(x)\) spit out \(3\)

rational
 one year ago
Best ResponseYou've already chosen the best response.3\[f^{1}(3) = a \implies f(a) = 3\] so you need to solve \(f(a)=3\) for \(a\)

rational
 one year ago
Best ResponseYou've already chosen the best response.3\[3 = 3+x^2+\tan(\pi x/2)\] \[0=x^2+\tan(\pi x/2)\] you can eyeball the value of \(x\) that satisfies above equation

rational
 one year ago
Best ResponseYou've already chosen the best response.3so \(f(0) = 3 \implies f^{1}(3) = 0\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow so much simpler than I was doing it before! Thank you

rational
 one year ago
Best ResponseYou've already chosen the best response.3hold up, we don't really need to find \(f^{1}(5)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And then solve for the inverse and then place into the original

rational
 one year ago
Best ResponseYou've already chosen the best response.3\(f\) eats \(f^{1}\)

rational
 one year ago
Best ResponseYou've already chosen the best response.3\[\require{cancel} \large { f(f^{1}(5))\\~\\ \cancel{f}(\cancel{f^{1}}(5))\\~\\5 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you sure they cancel?

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1they dont cancel they generate new function f(f^1(x))=x

rational
 one year ago
Best ResponseYou've already chosen the best response.3Think of it like this : \(f^{1}(5)\) is the value of \(x\) that makes \(f(x)\) spit out \(5\), so if you feed that value to \(f(x)\) again, it simply spits out \(5\)

rational
 one year ago
Best ResponseYou've already chosen the best response.3dw:1439073410822:dw

rational
 one year ago
Best ResponseYou've already chosen the best response.3dw:1439073520821:dw

rational
 one year ago
Best ResponseYou've already chosen the best response.3ofcourse assuming the inverse exists and onetoone etc..

rational
 one year ago
Best ResponseYou've already chosen the best response.3Notice that in part B, you are inputting \(5\) to \(f^{1}(x)\) (bottom box), it spits out \(x\), then you're inputting that value to \(f(x)\) again (top box) it spits out \(5\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok that makes sense. Thank you for your help

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I would like to know how to solve \(x^2 + tan (\pi x/2)=0\) . @rational please.

rational
 one year ago
Best ResponseYou've already chosen the best response.3plugin x = 0 and see that it evaluates to 0 i don't think there is a way to solve it analytically

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0ok, I got you. Since It is trivial when we graph them out. I would like to know whether we can solve it algebraically or not. Thanks for clarifying.
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.