what is the inverse function of f(x)=x ?

Question

And how to find an inverse function?

Answer 1

for finding the inverse replace f(x) by y. then solve for x.

The resulting function will be inverse.

inverse of f(x)=x is the same as x.

Answer 2

The inverse function in this case is itself, since swapping x and y results in the same function.

To find an inverse (which sometimes cannot be done explicitly/may not exist)

Let f be a function that is one-to-one over a particular domain.

1) Write y = f(x)

2) Change the subject to x

3) Swap x and y around (i.e replace x with y and each y with x, and that is your inverse function.



For y = x, (1)

x = y, (2) - making x the subject, and y = x (swapping x and y)

We see that the inverse is the same.

Geometrically, an inverse function is the original function reflected along the line y = x.

Note that y = x when reflected on the line y = x yields the same line.

Answer 3

Easiest way to find an inverse function is to switch the x's and y's and then resolve for y. In this case you have y= f(x)=x so the inverse in this case is also y=x. An inverse function is just a reflection of the original function over the line y=x so it makes sense that this is its own inverse.

Answer 4

To find the inverse of any function, switch the variables and solve for y or f(x). For this problem, it's the same equation.

Answer 5

to find the inverse, first let f(x) = y.



so, y = x.

Second, make x subject of formula.

in the above case x is already subject of formula.



then inverse of f is simply x.



for example, f(x) = x - 2



1st, let f(x) = y



y = x - 2



2nd, make x subject of formula,



x = y + 2



3rd, change the y into x

so, inverse of f-I(x) = x+ 2

Answer 6

If Jesus makes 1 dollar for every lawn cut and he cuts 3 in an hour how long will it take before his brother swims from Cuba to Miami?