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Contents
Inverse Functions
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Inverse Functions If f is a function, it will map a member x of set A onto a unique member y of set B. There is a function g that can make the return journey. But for g to exist, the range of f in B must be the entire set B, otherwise certain members of B would have no image in A under g. Also no member of B must have more than one arrow arriving from A, otherwise there would be more than one path back to A. Thus, for g to exist, it must be be a one-to-one function. When this occurs, we can find g. g is called the inverse function to f and we can write g = f-1.
Find f-1 in similar form for the
one-one function, f:x
Let y = 3x - 2
x = (y+2)/3
f-1 : x
(x + 2)/3
The functions f and
g are
defined by f:x
Two
functions f and g are defined by f:x (a) Find the expression of
f-1.
(b)
Given that g-1(3) = f-1(2) and that f-1g(4) = 1, find the value of
m and c.
 
f-1:x 
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Example 1
,x
1
and g:x
,x
