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

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. 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. Originally Posted by xfreekx
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.

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=.....

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

6. 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".

7. Originally Posted by mmm4444bot

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 ^^