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

]]>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 variablesâ€¦

...& at the time of plotting our coordinate pairs to sketch the graph of our inverse function , itâ€™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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