Consider the mapping f4 R rightarrow R where f4 x 1x2 4 Pr

Consider the mapping f_4: R rightarrow R where f_4 (x) = 1/(x^2 - 4). Prove that f_4 is not a function.

Solution

Since the domain of the function is R , and we do not have an image for x = 2 and x = -2 . Plus left hand limit and right hand limit both at x = 2 and x = -2 is different . Hence , the given function f₄(x) is not a function