Question

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

Answer 1

Answer:

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

$f(x)=f^{-1}(x)$