Math Is Fun Forum

ben1

Member

Registered: 2020-05-03

Posts: 1

inverse function & swapping x /y elements....

The question of why y and x should better be switched in doing an inverse function such as:

f(x) =  y = 2x+3
and its inverse
f-1(y)=  x =(y-3)/2,

we may consider that nstead of switching x & y , we could hang on to our inverse function as is and apply coordinate pairs with y as our independent and x as our dependent variables…

...& at the time of plotting our coordinate pairs to sketch the graph of our inverse function , it’d be reasonable to treat the x-axis as y-axis , our new independent variable, and y-axis as x-axis, the new dependent variable.

Ben Hidaji

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: inverse function & swapping x /y elements....

hi Ben,

Welcome to the forum.

When coordinates were invented (By Descartes) it was entirely arbitrary which went across and which up, and also which is the independent variable.  It's just a matter of what is usually done.

If you plot a function y = f(x) and also it's inverse y = f-1(x) on the same graph you will notice that each is a reflection of the other in the line y = x.  This can be a quite useful property, and you'd loose it if you kept x as a function of y.  But I take your point; it does seem odd to change things around after you've re-arranged the formula.

But the notation is just a way of telling people what the function is so the choice of letters is arbitrary too.

y = 2x + 3
x = 2y + 3
t = 2v + 3

are all describing the same function.

If you're asked to re-arrange a formula in an exam, read the question carefully to see what is expected.

Best wishes, stay safe,

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