Question

If G(x) = 3x + 1, then G^-1(1) is

Answer 1

One way in which to do this problem is to find the inverse function of G(x) first.  Another, faster, method is to look at G(x) = 3x + 1.  Find the x value for which y = 1:

1 = 3x + 1.  Then x must equal 0.  If (0, 1) satisfies G(x) = 3x + 1, then  (1, 0) satisfies the inverse function of G(x) = 3x + 1.  

Thus, the value of the inverse function with input 1 is 0.

Step 1:  Replace "G(x)" with y.

Step 2:  Solve the resulting equation for x.

Step 3:  Replace x with y and y with x.

                                                 -1

Step 4:  Replace this "y" with G    (x).  

Now replace "x" with "1".