1.1   Functions

EXERCISES

In problems #1-4, find the inverse function of each given function.

1.          Find  F^–1(x). 

2.          Find  f ^–1(x). 

3.          Find  g^–1(x). 

4.           Find  h^–1(x). 

In problems #5-14, refer back to the functions defined in problems #1-4… 

5.   F ( h (x) ) = ? 

6.   h ( F (x) ) = ? 

7.    g ( f  (x) )  = ? 

8.    F^–1 ( F (x) )  =  ? 

9.    g^–1 ( F^–1 (x) )  =  ? 

10.   h ( h (0) ) = ? 

11.   h ( h ( h (0) ) ) = ? 

12.   g ( g (0) ) = ? 

13.    f ( f (1) ) = ? 

14.  Let  M(x) = 2 – x² .     Then  M ( M (1) ) = ?   

For problems 15 through 22, suppose that g is an even function and f is an odd function.   For each problem, specify whether the given function is even, odd, or neither. 

15.    N(x) =  f (x) g(x)    

16.    M(x) =  f (x) g(x) + 1     

17.    y (x) = x f (x) g(x)    

18.    H(x) = g (f ( f (x) ) ) – g(x) + ( f (x) )²     

19.    V(x) =  x g(x) – f (x)    

20.     

21.     

22.     

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