Answer:
(g-f) (-1)= sqrt(15)
(f/g)(-1)= 0
(g+f)(2)=sqrt(3)-3
(g*f)(2)=-3*sqrt(3)
Step-by-step explanation:
We have to eval the expressions given in the point indicated.
Lets start by the first equation
(g-f)(-1)= g(-1) - f(-1)= =
Now, lest continue with the others
(f/g)(-1)= f(-1)/g(-1)= (1-1)/sqrt(15)=0
(g+f)(2)=g(2)+f(2)=sqrt(3)-3
(g*f)(2)=g(2)*f(2)=sqrt(3)*(-3)=-3sqrt(3)
Answer:
The inverse of a non-function mapping is not necessarily a function.
For example, the inverse of the non-function mapping is the same as itself (and thus isn't a function, either.)
Step-by-step explanation:
A mapping is a set of pairs of the form . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.
A mapping is a function if and only if for each possible input value , at most one of the distinct pairs includes
as the value of first entry.
For example, the mapping is a function. However, the mapping
isn't a function since more than one of the distinct pairs in this mapping include
as the value of the first entry.
The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping is the mapping
.
Consider mapping . This mapping isn't a function since the input value
is the first entry of more than one of the pairs.
Invert as follows:
In other words, the inverse of the mapping would be
, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)
Thus, is an example of a non-function mapping that is still not a function.
More generally, the inverse of non-trivial ellipses (a class of continuous non-function mappings, including circles) are also non-function mappings.
