Let a be a real number such that a + - - = 4. Find the value of the given expressions. (Note. They are integers.) ( a ) a2 + ( b) as + 3For any positive real number a > 0, how many distinct real roots does the equation x - a = 0 have?In the following figure, we plot the graphs of y = x, y = x , y = x , y = xandy = x2 determine (a, b). defined on [0, 1]. In particular, g and p are graphs of y = a" and y = a respectively. Please (1, 1) h g f p (0, 0) 0.5 (a, b) = v [MEH ] [ MEH ] 1 1/2 1/3Which of the followings represents the graph of y - cos (2x)? [ MEN ] AT50By = 2 cos x ME? Which of the followings represents the graph of y = 2 cos x? [ MEH ] NATOBEMy = COS (471 - 2x) JEFF ? Which of the followings represents the graph of y = cos (47 - 2x)? [ MEH ]The graphs of y = log2 x, y = 0.5%, y = 1.5%, y = 2" and y = 4 are given in the following diagram. (1) Which one of them represents the graph of y = 4*? (2) Which one of them represents the graph of y = 0.5? ( Answer ) : (1 ) [ MEN ] V : (2 ) [ MEH ] 6 V=X C b a 2 e 2 6\fLet A = log3 x, B = 4log, (3x ), and C - 12 + log3 (23 ). Find the value of a that would make the sequence { A, B, C} a geometric sequence. (a) 6 (b) 2 (c) 9 (d) none of the aboveLet { an j be a sequence such that log; (ait1 ) = i for all i . Find the value of log., (aN). (a) N( N +1 ) (b) N(N-1) 2 2 (c) N! (d) (N - 1)! O (a) O (b) O (c) O (d)On which of the following intervals is f(x) = log, (at 2 ) greater than or equal to zero? (Note. There might be multiple answers.) (a) (0, 1] (b) [1, 2] (c) [2, 3] (d) [3, 4] O (a) O (b) O (c) O (d)