Images of Functions

[jwsiii]

Can one value in the range of a function have more than one image? Ex: f(x)=x^2 Would the image of {9} be {-3,3}? The image of {4,9} would be {-3,-2,2,3} wouldn't it?

 

[lethe]

Originally posted by jwsiii
Can one value in the range of a function have more than one image? Ex: f(x)=x^2 Would the image of {9} be {-3,3}? The image of {4,9} would be {-3,-2,2,3} wouldn't it?

the image of {9} under x² would be {81} and the image of {4,9} would be {16,81}

the things you mentioned are instead preimages.

 

[ryans]

Exactly what Lethe said. The preimage of a function is only a function if there is a bijective mappring of the preimage onto the image. For example the inverse of the x^2 function is sqrt(x) only if you take either the set of positive reals including 0 to be your preimage. If you include the whole real line then there is a 2-1 mapping and we no longer have a function but rather a relation