Question

The range of the function f: f(X) = X-2 equals

a) R
b) R - {2}
c) R - {-1}
d) {-1}

Answer 1

The range of the function f(x) = x - 2 is all real numbers, denoted as R. No restrictions apply, as subtracting 2 from any real number still yields a real number.

Step-by-step explanation:

To find the range of the function f(x) = x - 2, we must consider the set of all possible output values of the function when the domain is all real numbers, denoted by R. The function f(x) simply shifts every input value x downwards by 2 units, which implies that for every real number x, there is a corresponding y value that is two less than x. There is no restriction on the values that x can take; x can be any real number, so subtracting 2 from any real number will also result in any real number. Therefore, the range of the function is all real numbers as well.

The correct answer is a) R, which represents the set of all real numbers as the range of the function f.