Discrete Mathematics I have tried to do the question but not

Discrete Mathematics

I have tried to do the question but not sure the answer is right or not.

(a) the range of f is f(x) = {0}, for x is element of Z

so f(A) = {0}.

(b) the range of f is f(q,r) = {Z}, (not sure about this, I\'m assign the value like:

f(q,r) = 2q + 3r for q,r is an element of Z, and found out the domain range will be every integer number (Z)

but how can I write the proper answer? Is f(A) = {Z} the right way for mathematical expression for this answer?

(c) the range of f is f(x) = for x is element of R (real number)

so the range f(x) = { cube root of all x}, how to display this?

(d) don\'t know how to display the answer f(a/b) = {all R numbers of 2a/b}? R = real numbers

(e) don\'t know how to display too.

26. For appropriate sets A and B, determine the range of a function f : A B that assigns (a) to each integer the sum of that integer and its negative. (b) to each pair of integers the sum of twice of the first integer and three times the second integer (c) to each real number the cube root of that number (d) to each rational number two times that number (e) to each positive 2-digit integer the first digit of that integer.

Solution

Q 26 a) Sum of a number and its negative = a+(-a) = 0.
So f(x)= 0 , for all x which are Z. So range is all numbers.

(b) f(x,y)= 2x+3y where both x and y are integers.
if x and y are integer then f(x,y) are integer and if x and y are natural number then f(x,y) is a natural number so the range of x and y is -infinity to +infinity depending upon x,y

(c) f(x)= (cube root of x) . here again x ranges from -infinity to +infinity and includes all natural numbers.

(d) f(x) = 2x, Range of f(x) is all rational number ranging from -infinity to +infinity.

(e) f(x) = x/10, here 9<x<100 and 0<f(x)<10 where x and f(x) are both integers.