ASSIGNMENT 1

1. What is the Cartesian product of the set of real numbers and itself?
Ans : The Cartesian product is every ordered pair in all of the quadrants of the coordinate plane. 2. What is the domain and range of the relation {(2, 4),(4, 8),(8, 16)} ?
Ans: domain {2,4,8} and range {4,8,16} and the function can be given as f(x)=2x. 3. Decide whether the graph below is a function.

Ans: The above shown graph is not a function since for a given x value it has multiple y values at certain points and hence cannot be a function. 4. What is the domain and range of the function f (x) = ?
Ans: domain 0 ≤ x and range 0 ≤ f(x) 5. Is the following a function: y = ± x ?
Ans : No it is not a function for a given x value it has two Y values . 6. Is the function f (x) = 4x even, odd, or neither? Ans : function f (x) = 4x is an odd function since f (x) = - f (- x) 7. Is the function f (x) = x - 5 even, odd, or neither?
Ans : function f (x) = x - 5 is neither neither even nor odd. 8. What is the inverse of the function y = , and is it a function?
Ans : The inverse is y = x2 +1 and It is a function. 9. A piecewise function is defined this way: f (x) = - x for x < 0 , f (x) = x2 for 0 ≤ x ≤ 3 , f (x) = 3x for x > 3 .
What is f (- 4) + f (3) + f (7) ? Ans : -4 + 9 +21 = 26 . 10. Let f (x) = - 2 and g(x) = x + 1 . What is (f o g)(x) and (g o f )(x) ?
Ans : (f o g)(x) = 3x+1 - 2 (g o f )(x) = 3x -1