Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

Inverse Functions. Why rewrite as y=f(x)

What does this mean? And does it have to be y?

By rewriting, for example, f(x)=2x+3, as y=2x+3, are we simply stating that something = 2x+3; and in the first case we’re calling that something f(x), and in the second case we’re calling it y?

Does the y have anything to do with the y axis in x,y coordinates? Or is just a randomly chosen letter? Could it just as well be z, or a, or b, etc?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: Inverse Functions. Why rewrite as y=f(x)

y and f(x) are interchangeable here. I think y is used because of x-y graphs.

But a graph doesn't have to use x and y; you could use v and t for example (v = u + at in mechanics)

Why the re-write?

I find it easier to change the subject if it starts y =

example.  Change the subject of this equation ie x = ?

Collect all the x terms on one side and everything else on the other

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Re: Inverse Functions. Why rewrite as y=f(x)

What does this mean? And does it have to be y?

By rewriting, for example, f(x)=2x+3, as y=2x+3, are we simply stating that something = 2x+3; and in the first case we’re calling that something f(x), and in the second case we’re calling it y?

Does the y have anything to do with the y axis in x,y coordinates? Or is just a randomly chosen letter? Could it just as well be z, or a, or b, etc?

Note: y and f(x) mean the same thing. It's like saying car and automobile.

For example, y = 2x + 5 can also be written as f(x) = 2x + 5. In terms of functions, f(x) is mostly used.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Inverse Functions. Why rewrite as y=f(x)

Inverse Functions. Why rewrite as y = f(x)?

What does this mean? And does it have to be y?

Youre working with inverse functions which means that you started with a function f(x)
(it doesn't have to be 'f(x)'; it can be g(x), h(x), etc; f(x) is the most common name)
Its easier to do the algebra to find the inverse when you rename f(x) as y
youre finding the inverse function so you solve for x in terms of y
then you swap the variables and rename the new y as f^(-1)(x)
but whatever the name for the function -- y, f(x), f^(-1)(x), Q(x) -- its all the same thing
You pick the value for the input (almost always x) and figure out the value of the output (which you graph on the vertical axis)

paulb203

Member

Registered: 2023-02-24

Posts: 136

Re: Inverse Functions. Why rewrite as y=f(x)

Thanks, guys.