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**ben1****Member**- Registered: 2020-05-03
- Posts: 1

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

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,914

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

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