Calculus Problem Set

Question 1:   Find the parameters a and b included in the linear function f(x) = a x + b so that f -1 (2) = 3 and f -1 (-3) = 6, where f -1 (x) is the inverse of function f.

Question 2:   Given f(x) = x3 + 2 x, complete the table of values given below and find f -1(3) and f -1(- 12). 

x	f(x)
0	0
1	3
2	12

Question 3:  Proove that the inverse of an invertible odd function is also an odd function.

Question 4:   Let f(x) = 1 / (x - 2). Find the points of intersection of the graphs of f and that of f -1 the inverse of function f. Graph f, its inverse and the line y = x. Where are the points of intersection located?

Question 5:   Graph function f defined by f(x) = |x - 2| + 2x and its inverse f -1 and find a formula for its inverse.