IB HL Math Homework #4: Functions and Equations Assigned: 9/20/07, Thursday Due: 9/25/07, Tuesday 1) Find all of the values of x that satisfy the inequality 2x 1. | x 1| 2) The polynomial f(x) = x3 + 3x2 + ax + b leaves the same remainder when divided by (x – 2) as when divided by (x + 1). Find the value of a. 3) The functions f and g are defined by f : x e x , g : x x 2. Calculate (a) f 1 (3) g 1 (3) (b) ( f g ) 1 (3). 4) A sum of $5000 is invested at a compound interest rate of 6.3% per annum. (a) Write down an expression for the value of the investment after n full years. (b) What will be the value of the investment at the end of five years? (c) The value of the investment will exceed $10000 after n full years. (i) Write an inequality to represent this information. (ii) Calculate the minimum value of n. 5) Let f ( x) f ( x) g ( x) . x4 x2 , x 1 and g ( x) , x 4 . Find the set of values of x such that x 1 x4 6) Given that (x – 1) and (x – 2) are factors of 6x4 + ax3 – 17x2 + bx – 4, find a and b, and any remaining factors. 7) Consider the functions f ( x) e 2 x and g ( x) sin x 2 . (a) Find the period of the function f g. (b) Find the intervals for which ( f g ( x)) 4. 8) The function f is defined on the domain [-1,0] by f : x (a) Write done the range of f. 1 . 1 x2 (b) Find an expression for f-1(x).