Question

Show that the function of f(x) = a - x is its own inverse for all real numbers a

Answer 1

f(x) = a - x

y = a - x

y + x = a - x + x

y + x = a

y + x - y = a - y

x = a - y

f-¹(x) = a - x

Answer 2

The inverse of a function is the opposite of the function.

See below for the proof of: $\mathbf{f(x) = f^{-1}(x)}$

The function is given as:

$\mathbf{f(x) = a - x}$

Rewrite as:

$\mathbf{y = a - x}$

Swap x and y

$\mathbf{x = a - y}$

Make y the subject

$\mathbf{y = a - x}$

Rewrite as:

$\mathbf{f^{-1}(x) = a - x}$

Hence:

$\mathbf{f(x) = f^{-1}(x) = a - x}$

Read more about inverse functions at:

https://brainly.com/question/10300045