Combining Functions

1. Let f(x) = 2x-3 and g(x) = x2 - x - 6. Find

(i) (f+g) (x). (ii) (f-g)(x) . (iii) (fg)(x).
(iv) (f / g) (x). (v) the domain of (f+g). (vi) the domain of (f/g).

 

2.

(i) (f+g) (x). (ii) (f-g)(x) . (iii) (fg)(x).
(iv) (f / g) (x). (v) the domain of (f+g). (vi) the domain of (f/g).

 

3.

(i) (f+g) (x). (ii) (f-g)(x) . (iii) (fg)(x).
(iv) (f / g) (x). (v) the domain of (f+g). (vi) the domain of (f/g).

 

4. (i) Using f and g from problem 1 above, find if possible (f+g)(2) .

(ii) Using f and g from problem 2 above, find if possible (fg)(1).

(iii) Using f and g from problem 3 above, find if possible(f/g)(0)

5.

Using the graphs of the functions f and g above, find if possible

(i) (f+g) (-1). (ii) (f.g)(2) . (iii) (f/g)(0).
(iv) find the domain of f. (v) the domain of (f+g). (vi) the domain of (f/g).

6. Two function f and g are listed in table form below

x -2 -1 0 1 2 3
f(x) 3 0 2 -1 4 2
 
x -1 0 1 2 3 4
g(x) -1 3 0 4 2 1

a) Assumming that the above tables completely describe the functions f and g, find the domain of f + g.

b) Assumming that the above tables completely describe the functions f and g, find the domain of f / g.

c) Find if possible (f - g)(3) .

d) Find if possible (f.g)(2).

e) Find if possible (f/g)(2)

7. a) Let f(x) = 2x - 3 and g(x) = x2 - x - 6. Find (f o g)(x) , (g o f)(x) and (f o f)(x) .
  b)
  c)

 

8.a) Using the functions f and g in problem 5 above , find (f o g)(2) and (g o f)(3).

b) Using the functions f and g in problem 6 above , find (f o g)(3) and (g o f)(3).

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