f . – . Find the domain of the function f ( x ) x – x . Find the domain and the range of the real function f defined by f ( x ) = ) x − .
Find the domain and the range of the real function f defined by f ( x ) = – . Let , : f ∈ R be a function from R into R . Determine the range of f . .
Let f , g : R → R be defined, respectively by f ( x ) = x + , g ( x ) = x – . Find f + g, f – g and f g . . Let f = {( , ), ( , ), ( ,– ), (– , – )} be a function from Z to Z defined by f ( x ) = ax + b, for some integers a , b .
Determine a , b . . Let R be a relation from N to N defined by R = {( a , b ) : a , b ∈ N and a = b }. Are the following true?
( a , a ) ∈ R, for all a ∈ N ( a , b ) ∈ R, implies ( b , a ) ∈ R (iii) ( a , b ) ∈ R, ( b , c ) ∈ R implies ( a , c ) ∈ R. Justify your answer in each case. . Let A ={ , , , }, B = { , , , , , } and f = {( , ), ( , ), ( , ), ( , ), ( , )} Are the following true?
f is a relation from A to B f is a function from A to B. Justify your answer in each case. RELATIONS AND FUNCTIONS . Let f be the subset of Z × Z defined by f = {( ab , a + b ) : a , b ∈ Z }.
Is f a function from Z to Z ? Justify your answer. . Let A