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How to Find Inverse Function in Higher Mathematics
The function is actually the corresponding relationship between two data sets, and the inverse function is actually based on the original function, which does not change the corresponding relationship between the two data sets, but only changes the positions of the corresponding parties: it turns out to be.

X 1→y 1, X2 → Y2 ... Now it is.

y 1→x 1、y2→x2……

The former is the original function and the latter is the inverse function-this is an expression of the function: enumeration. Visible, anti-function

"domain"

and

"range"

It exchanges with the original function.

As you can imagine, not all functions have original functions. Functional authority

"many to one"

Relationships appear, but they are not allowed.

"One-to-many". So, all functions with inverse functions are

"one-to-one correspondence"

The relationship. It can be simply understood as functionality.

"domain"

and

"range"

The number of elements in is equal and can be matched one by one.

Hypothetical function

y

=

f(x)

(The standard notation of this function is: f:x→y) It has the inverse function: ψ: y → x. So, F.

Functional image of

f

and

talent

Functional image of

w

The following relationship must be satisfied: point (x, y) is on f and only if point (y, x) is necessarily on f.

w

Let's go

Obviously, these two points are about straight lines.

y

=

x

Symmetry. When?

f

All the points in the world can be found in

w

When an axisymmetric point is found on F.

and

w

It is axisymmetric in itself, which is exactly the case.

Finally, the two axisymmetric images must be "consistent".