1 Given two relations The circles are supposed to represent

1.) Given two relations (The circles are supposed to represent composition of functions)

f = {(1,2),(3,4),(4.5)}

g ={(3,2),(1,4),(2,2),(5,4)}

a) Which relation is a function?

b) Find the range of f (This is a set of numbers)

4.) We say that a function is invertible if the inverse of the function (as a relative) is also a function. Find the inverse (relation) of the following function. Is the function f invertible? Explain. f = {(1,2),(3,2),(5,5),(6,1)}

5.) One can show that function f(x) = 2x + 1 is invertible. Let f ^-1 denote the inverse function of f.

a) f^-1(7)

b) Find the expressions for  f^-1(x). [Suggestion: Our goal is to write the equation y =  f^-1(x) which is just the same equation as x = f(y)]

6) What is the domain of the inverse of the function f(x) = 2 + ?x ?(The domain of the inverse of a function is (always) the range of that function)

Solution

3) fog(x) = 2[x/(x-2)]/([x/(x-2)] + 1)

= x/(x-1)

now for this to be defined f(x) and g(x) both also should be defined.

so x can not be equal to -1,1,2

so domain of fog(x) = R - {-1,1,2}