1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse trig function

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data
    My problem is as follows:
    find the inverse of
    [tex] 3x+1+\sin(x)[/tex] with the domain [itex][-\frac{\pi}{2},\frac{\pi}{2}][/itex]


    2. Relevant equations



    3. The attempt at a solution
    for this would I just try to solve as normal by setting y=f(x) then using the fact that [itex]\arcsin(x) = y[/itex] or is this the wrong way of solving this?
     
  2. jcsd
  3. Jan 8, 2012 #2

    Mark44

    Staff: Mentor

    You're not going to be able to solve the equation y = f(x) = 3x + 1 + sin(x) for x (to get the inverse x = f-1(y).
    What is the exact problem statement? It might be that you are misreading what is being asked for in this problem.
     
  4. Jan 8, 2012 #3
    The exact wording for this problem:
    [itex]f(x) = 3x + 1 + \sin(x)[/itex] with domain [itex][-\pi/2, \pi/2][/itex]. Without your calculator, determine the value of [itex]f^{-1}(1)[/itex].

    Since this is an inverse function, I was going to try to solve for the inverse function, then solve for [itex]f^{-1}(1)[/itex]
     
  5. Jan 8, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How is this question related to a problem which requires you to:
    Solve [itex]f(x)=1\text{ for }x\,.[/itex]​
    ?
     
  6. Jan 8, 2012 #5
    To which question are you referring? I never mentioned having to solve [itex]f(x)=1[/itex]
     
  7. Jan 8, 2012 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The problem asks to determine f-1(1)=x. The equation is equivalent to 1 =f(x), that is, 3x+1+sin(x)=1. Solve for x.

    ehild
     
  8. Jan 8, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I'll state it more clearly.

    How are the following two problems related?
    Determine the value of [itex]f^{-1}(1)\,.[/itex]

    Solve [itex]f(x)=1\text{ for }x\,.[/itex]​
     
  9. Jan 8, 2012 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    While that is the general method, if you are lucky the problem is one that can be solved by recognizing it to be a special case that is easy to solve without ploughing all the way through the full general method (even if the general method were possible).

    So you are being asked to find the x value (or values) that makes

    [itex]3x + 1 + \sin(x) = 1[/itex]


    Play around with that equation to see whether you can knock it into something that speaks meaningfully to you. :smile:
     
  10. Jan 8, 2012 #9
    Ah, I see what you guys are talking about now. Thanks for the help. Much appreciated.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inverse trig function
  1. Inverse Trig Function (Replies: 3)

  2. Inverse Trig Function (Replies: 5)

Loading...