Suppose f : A rightarrow B is a function, If C A, define as is called the image of C under f and
is the set of all possible outputs that can occur when the inputs come from the set C. Similarly, if
D B, defined as is called the inverse image of D under f and is the set of all possible inputs in A
that will be outputs that belong to the set D. where D is a subset of the target set (co-domain) B.
If f : R rightarrow R is defined by f(x) = x2, then what is ({2, -2, 3}) ? what is ({4, 9}) ?
Solution
The "image of f under C" refers to the values of f(x) that you get when you plug in the values of
x that are in C. For f(x) = x2, when you plug in 2, -2, and 3, you get 4, 4, and 9. The image of f
under {2,-2,3} is therefore {4,9}.
The "inverse image of D under f" refers to all the values of x that could give you the numbers in
D as your f(x). If f(x)=x2=4, then x must have been -2 or +2; if f(x)=x2=9, then x must have
been -3 or +3. Thus, the inverse image of {4,9} under this f is {-3,-2,2,3}.
I hope this is clear!