Inverse Functions

Let f(x)=3x+4 and g(x)=2x-3. If h(x)=f(g(x)), then what is the inverse of h(x)?

f(g(x))  means to put the function g  into  f

h(x)  = f(g(x))  = 3 [ 2x - 3 ]  + 4   =   6x - 9 + 4  =  6x - 5

So

h(x)  = 6x  - 5      for  h(x), write y

y  = 6x  - 5        we want to get x by itself...add 5 to both sides

y + 5  = 6x       divide both sides by  6

[ y + 5 ] / 6    = x         "swap" x and y

[ x + 5 ] / 6  = y      and this is the inverse of  h