1. Can the composition pres \circ lady be defined? What about lady \circ pres?
2. Which of the following functional inverses exist and which do not? pres^{-1}, lady^{-1}, (lady \circ pres)^{-1}, (pres \circ lady)^{-1}
1:
The composition pres \circ lady cannot be defined since the value of the function lady has the name of a first lady as a function value, but the function pres has the dates of presidential inauguration as domain values.
The composition lady \circ pres can be defined. The function pres has range values from P, which can be substituted into the function lady.
2:
(pres \circ lady)^{-1} will not exist, because pres o lady is undefined. (lady \circ pres)^{-1} exists, because any first lady can be matched
2. Which of the following functional inverses exist and which do not? pres^{-1}, lady^{-1}, (lady \circ pres)^{-1}, (pres \circ lady)^{-1}
1:
The composition pres \circ lady cannot be defined since the value of the function lady has the name of a first lady as a function value, but the function pres has the dates of presidential inauguration as domain values.
The composition lady \circ pres can be defined. The function pres has range values from P, which can be substituted into the function lady.
2:
(pres \circ lady)^{-1} will not exist, because pres o lady is undefined. (lady \circ pres)^{-1} exists, because any first lady can be matched