Afunction f(x)=3x+12.
a determine the inverse of this function and name it g(x)
b. use composite functions to show that these functions are inverse
c. evaluate f(g(- explain? what is the domain?

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•  Function:   f(x) = 3x + 12.

A.  Finding the inverse of f.

The composition of f with its inverse results in the identity function:

(f o g)(x) = x

f[ g(x) ] = x

3 · g(x) + 12 = x

3 · g(x) = x – 12

              x – 12
g(x)  =  ⸺⸺
                 3

               x 
g(x)  =  ⸺  –  4    <———    this is the inverse of f.
               3

________

B.  Verifying that the composition of f and g gives us the identity function:

•  



and also

•  



________

C.  Since f and g are inverse, then

f(g(– 2))

= (f o g)(– 2)

= – 2          ✔


•  Call h the compositon of f and g. So,

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

h(x) = x

As you can see above, there is no restriction for h. Therefore, the domain of h is R (all real numbers).

I hope this helps. =)

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