(1) Solve the following inequality. Use interval notation to express the result. 2x + 1- (2) Find the domain of the following function. Express the domain using interval notation. f(x) = V5 -x+ 1 I' - 31 (3) Suppose (9) Suppose f(x) = vix - 8 and g(x) = - . Find (fog)(x) and its domain. /(I) = |x -3| +4 ifz 0 (c) Find the range of f. and use the graph to determine whether f is one-to-one or not. Explain. (4) The graph of g is shown below. (7) The graph of f is shown below. (a) Sketch the graph of f-1 on the same diagram. (b) Evaluate fo f(0). (c) Evaluate f-1(2). 19 3 -2 -1 -5 -14 -3- (a) Find g(1) and g(2). b) Find all r such that g(x) = 2. (c) Write the domain of g using interval notation. (5) Alice runs a candy store and she carries only two flavours lemon and strawberry, which she sells for L(k) and S(k) dollars, respectively, for & kilograms. Assume that both functions are one-to-one. (11) Suppose f(z) = 25 + x3 + 2. Find f '(2). (a) What is a practical interpretation of L-1(10)? (b) Jack bought C' kg of candies. If he spent $30 on lemon candies, find an expression (in dollars) for the amount he spent on strawberry candies. (The expression may include C.) (6) The point (5,3) is on the graph of /(x). Find the corresponding point on the graph of g(x) = 5/(-3x + 2) -4