Question

Determine if the two functions are inverses of one another.

Answer 1

Note :

Two functionsf (x) and g (x) are inverse functions if and only if both of their compositions are the identity function.

f o g (x) = g o f (x) = x.

The functions are f( x ) = - 2x + 1 and g (x) = (x - 1)/2.

Now plug the formula for g(x) into every instance of "x" in the formula for f (x) :

f o g (x) = f (g (x) )

= f ( (x - 1)/2)

= - 2(x - 1)/2 + 1

= - x + 1 + 1

= - x + 2.

→ f o g (x) = - x + 2.

Now plug  the formula for f (x) into every instance of "x" in the formula for g(x) :

g o f (x) = g (f (x) )

= g (- 2x + 1)

= ((- 2x + 1)- 1)/2

= - 2x/2

= - x.

→ g o f (x) = - x.

∴ f o g (x)  ≠  g o f (x) ≠ x.

So, the given two functions are not inverses of each other.