## Definition 1.2.4: Image and Preimage

Let

**A**and**B**be two sets and*f*a function from**A**to**B**. Then the**image**of*f*is defined as*imag(f) = {b*B : there is an a**A**with*f(a) = b*}.

**A**and**B**be two sets and*f*a function from**A**to**B**. If**C**is a subset of the range**B**then the**preimage**, or**inverse**image, of**C**under the function*f*is the set defined as*f*(^{-1}**C**) = {*x***A**:*f(x)***C**}