Solutions

Problem Set 9

Functions

 

 

For each function given, decide if it has an inverse and find it’s inverse, for those that do. Verify your result by direct substitution.

 

a)      f(x)  = 9x  +2                 f-1(y) = y/9 – 2/9

 

b)      f(x) = x3  + 9                  f-1(y) =

 

c)       f(x) =  x2                         no inverse  (fails horizontal line test)

 

d)      f(x) =  5                           no inverse  (graph is a horizontal line)

 

e)       f(x) =  1/(x-5)           domain all x except 5.    f-1(y) = 1/y + 5