Suppose the function ƒ has the property that IS(x) – S()| < |x -|| for each pair of points x, t in the interval (a, b). Prove that f is continuous on (a, b).

Let f (x) = {²³ +1 -X for the interval [-1,1]. for x < 0 for x ≥ 0 Determine whether or not the IVT applies to show that the given function takes on all values between f(-1) and f (1) for x = (-1,1). The Intermediate Value Theorem applies The Intermediate Value Theorem does not apply

Let f : [a,b] → [a,b] be continuous. Prove that the Range of f is a closed interval.

Let f(x) = 1 202/1-x2022 -. Evaluate ƒ(ƒ(ƒ(.…..(ƒ(2022))….))), where there are 2022 fs.