Consider the following for the two (02) items that follow: Let the function f(x) = x^2 - 1 . What is _ x 1 f f(x) equal to?

Step-by-step solution

Given f(x) = x^2 - 1 . The composite function f f(x) is given by: f(f(x)) = f(x^2 - 1) = (x^2 - 1)^2 - 1 Since f(f(x)) is a polynomial and continuous everywhere, the limit can be evaluated by direct substitution: _ x 1 f f(x) = f(f(1)) f(1) = 1^2 - 1 = 0 f(f(1)) = f(0) = 0^2 - 1 = -1 Thus, the limit is -1 . Answer: -1