The letter x is traditionally used as the independent variable, so when we concentrate on the inverse rather than on the regular fcn, we usually reverse the orders of x and y: f^(-1)[x] =y f(y) = x f^(-1)(f(x)) = x How did they get the above?

Question

The letter x is traditionally used as the independent variable, so when we concentrate on the inverse rather than on the regular fcn, we usually reverse the orders of x and y:

f^(-1)[x] =y <=> f(y) = x

f^(-1)(f(x)) = x
How did they get the above?

anonymous · Answer

Just to point out, the f^(-1)[x] is the inverse.

amistre64 · Answer

Descartes was prone to use alchemy symbols

anonymous · Answer

Ok I am saying that say g(x) is the inverse of f(x)

anonymous · Answer

then f(x) = a, so g(a) = x

anonymous · Answer

So what are they subbing in when they do f(g(x))?

amistre64 · Answer

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anonymous · Answer

This says that in the function, where you see a, you put in g(x)?

amistre64 · Answer

spose a is an element of x; then f(a) maps onto an element in y

amistre64 · Answer

the inverse undoes the process; and send the value of f(a) from its place in the set of y, and sends it back to its original place in the set of x

amistre64 · Answer

since f(x) = y; we can rightly say; f-1(f(x)) = x