Answer:
Step-by-step explanation:
Let and , we proceed to derive and by algebraic means:
(i)
1) Given
2) Modulative property
3) Existence of additive inverse/Associative property
4) Distributive property
5)
6) Definition of subtraction
7) Composition of functions/Result
(ii)
1) Given
2) Modulative property
3) Existence of additive inverse/Commutative and associative properties
4) /
5) Definitions of division and power
6) Modulative property
7) Existence of additive inverse/Associative property
8) Perfect square trinomial
9) Addition of homogeneous fractions.
10) Composition of functions/
11) Definitions of division and subtraction/Result
Now we find the inverse of :
1) Given
2) Compatibility with addition
3) Definition of substraction/Commutative and associative properties
4) Existence of additive inverse/Modulative property
5) Compatibility with multiplication/Commutative and associative properties
6) Existence of multiplicative inverse/Modulative property
7) Symmetrical property/Notation/Result
Finally, we proceed to calculate :
1) , Given
2) Composition of functions
3) Result