5_ Let X be a normal topological space, let E be a closed subset of X, and let f: E -> R be continuous. Show that f can be extended to continuous function from X to R. Hint: Let g: R -> (-1,1) be a homeomorphism, extend g ∘ f to a map from X to [-1,1], and decide what to do on the set where the extension assumes the values ±1.