6. (15 points) If f: R + R is a function, its square f2 : R R is defined by f?(x) = f(x)2. In parts (a) and (b), decide if the statements are true or false. If the statement is true, prove it. If the statement is false, give a counterexample. (a) If a sequence of functions fn : R+R converges uniformly to g(x) = x on R, then the sequence of squares f. converges uniformly to the function g (x) = x2 on R. (b) If a sequence of functions fn: R + R converges uniformly to a bounded function g on R, then the sequence of squares fa converges uniformly to the function g2 on R. 6. (15 points) If f: R + R is a function, its square f2 : R R is defined by f?(x) = f(x)2. In parts (a) and (b), decide if the statements are true or false. If the statement is true, prove it. If the statement is false, give a counterexample. (a) If a sequence of functions fn : R+R converges uniformly to g(x) = x on R, then the sequence of squares f. converges uniformly to the function g (x) = x2 on R. (b) If a sequence of functions fn: R + R converges uniformly to a bounded function g on R, then the sequence of squares fa converges uniformly to the function g2 on R