Question

Is the function f(x) = -x its own inverse?
amos @audreyw2014

Answer 1

No, the function f(x) = -x is not its own inverse.

Step-by-step explanation:

No, the function f(x) = -x is not its own inverse. In order for a function to be its own inverse, the composition of the function with itself must result in the identity function. In this case, when we compose f(x) with f(x), we get f(f(x)) = -(-x) = x. This is not equal to the identity function, which is y = x. Therefore, f(x) = -x is not its own inverse.

Answer 2

f(x) and its inverse are the same

Step-by-step explanation:

The inverse function

If y=f(x), the inverse function
`f^(-1)(x)` is defined such as

`f(f^(-1)(x))=x`

To find the inverse function, there is a practical method:

a) Change letters x for y and vice-versa

b) Isolate y in terms of x only

c)
`y=f^(-1)(x)`

In our case,
`y=f(x)=-x`

a) Interchanging letters

`x=-y`

b) Isolate
`y=-x`

c)
`f^(-1)(x)=-x`

As we can easily see, f and its inverse are exactly the same

`f(x)=f^(-1)(x)`