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 ) = - 3x + 2 and g (x) = (x + 2)/3.

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 + 2)/3)

= - 3(x + 2)/3 + 2

= - x - 2 + 2

= - x.

→ f o g (x) = - x.

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 (- 3x + 2)

= ((- 3x + 2) + 2)/3

= (- 3x + 4)/3.

→ g o f (x) = (- 3x + 4)/3.

∴ f o g (x)  ≠  g o f (x) ≠ x.

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