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/3

= x.

→ g o f (x) = x.

∴ f o g (x) =  g o f (x) = x.

So, the given two functions are inverses of each other.