Results 1 to 7 of 7

Thread: Find t for which f(t) = g(t) in equation form

  1. #1

    Find t for which f(t) = g(t) in equation form

    Hey,

    I don't have a quation about the actual math, but about the way of writing the equation.

    I want to find the time T for which two functions f(t) and g(t) are equal.
    But I want to write T as a function or something so:

    T = t "for which" f(t)=g(t), or
    T -> f(T)=g(T), or

    ????

    Is there a nice way of writing this mathematically??

    So what I'm saying is I need an equation/expression for the independant variable t.

    Thanks

  2. #2
    To clarify,
    I want to be able to express: " I want to find the time T for which two functions f(t) and g(t) are equal." in mathematical symbols or something.

    I know that you can write stuff like "for all A there exist a B that is larger than C" with math symbols.

    I want to write something like:

    T = .........

    From which it is clear that I mean that T is the time at which the 2 functions f(t) and g(t) are equal.

  3. #3
    Elite Member mmm4444bot's Avatar
    Join Date
    Oct 2005
    Location
    AZ, Seattle, San Diego
    Posts
    10,075
    Quote Originally Posted by xfreekx View Post
    I want to be able to express:

    "I want to find the time T for which two functions f(t) and g(t) are equal." in mathematical symbols or something.
    Are you sure you need two different symbols for time?

    If symbol t is already defined as a time variable, then writing, "I want to find all t such that f(t)=g(t)", would be a clear statement that you're trying to solve the equation for time.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  4. #4
    with f(t) and g(t) I mean two functions of time variable t.
    With T I mean the value t needs to take in order to game f=g.

    I am not interested in the math or the calculation, I know how to do it.
    I just want to put it in a question without words.
    So say f(t) is the position of car 1 and g(t) is the position of car 2.
    Car 1 is behind car 2 but is moving faster. The the question would be:
    Find the time T at which f(t)=g(t).
    But I dont want to put in the words, I want to put in math symbols so that I can just say:
    The time it takes for car 1 to overtake car 2 is:

    T = .......

    And on the dots I want an expression which indicates: t for which holds that f(t)=g(t).
    On the dots I dont want a number, I want an expression indicating the problem.

    So I want to put:
    "T=t for which f(t)=g(t)" into an expression of some sort: T=.....

  5. #5
    Elite Member
    Join Date
    Sep 2012
    Posts
    3,015
    You have already been given the answer

    [tex]\text {Find } t \text { such that } f(t) = g(t).[/tex]

  6. #6
    Elite Member mmm4444bot's Avatar
    Join Date
    Oct 2005
    Location
    AZ, Seattle, San Diego
    Posts
    10,075
    You didn't answer my question about a need for two symbols.

    If there's only one solution, and you don't want to state its numerical value, and you want to distinguish between the variable t and a constant T (the solution), then you could write the following.

    The time it takes is T | f(T) = g(T)

    or

    The time it takes is T : f(T) = g(T)

    These are each read as, "The time it takes is T, such that f of T equals g of T". Make sure your audience knows how to interpret the symbol for "such that"; otherwise, it's better to spell out the phrase "such that".
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  7. #7
    Quote Originally Posted by mmm4444bot View Post
    You didn't answer my question about a need for two symbols.

    If there's only one solution, and you don't want to state its numerical value, and you want to distinguish between the variable t and a constant T (the solution), then you could write the following.

    The time it takes is T | f(T) = g(T)

    or

    The time it takes is T : f(T) = g(T)

    These are each read as, "The time it takes is T, such that f of T equals g of T". Make sure your audience knows how to interpret the symbol for "such that"; otherwise, it's better to spell out the phrase "such that".


    Thanks this is what I needed ^^

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •