Can you help me with this Real Analysis problem, please?(Can you have the answer written too, please? I feel like I can read it easier that way. Thank you very much!)

Question 6 (Mandatory) (7 points) S > Let [a,b] be a closed and bounded interval, let ke R, and let f:[a,b] =R be a function. Suppose that f satisfies the conclusion of the intermediate value theorem. Show that the function g(x) defined by g(x) = kf(x) for all x=[a,b] also satisfies the conclusion of the intermediate value theorem