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

To clarify,
I want to be able to express: "[FONT=wf_segoe-ui_normal] 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.[/FONT]

xfreekx said:

I want to be able to express:

"[FONT=wf_segoe-ui_normal]I want to find the time T for which two functions f(t) and g(t) are equal." in mathematical symbols or something.[/FONT]

Click to expand...

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.

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=.....

You have already been given the answer

\(\displaystyle \text {Find } t \text { such that } f(t) = g(t).\)

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".

mmm4444bot said:

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".

Click to expand...

Thanks this is what I needed ^^