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QUESTION 1 1.1 Prove that x+ 2a is a factor of the expression: f(x)=x' +4ax' -ax+4a*x-2a' (3) 1.2 If ax + bx+ c =0, make x the subject of the formula (solve for x) by means of completing a square. (7) 1.3 A retailer wishes to buy a maximum of 20 guitars. He/She can buy either type A for R1 500 each or type B for R3 000 each. R45 000 has been set aside for the purchase of the guitars. However, at least 6 of each type must be purchased. 1.3.1 If the retailer buys x guitars of type A and y guitars of type B. write FOUR inequalities which satisfy the above conditions. (4) 1.3.2 Represent the inequalities graphically and indicate the feasible region. Scale: Icm = 2 guitars (5) 1.3.3 If the retailer makes a profit of R400 on each guitar of type A and R1 000 on each guitar of type B, write an equation for the profit (P) and hence determine how many of each type he/she should buy to make a maximum profit. (4) 1.4 During a class exercise Simon correctly constructed the graph of y = x'. Below is the graph he drew. 1.4.1 Write the equation of the axis of symmetry for the graph of y = x' . (2) 1.4.2 Determine the equation of the inverse of the function y = x'. (2) 1.4.3 Sketch the inverse of the function y = x' (6) 1.4.4 Is the inverse function continuous or discontinuous? (1) QUESTION 2 2.1 3 Given the determinant: 4 - 2 Determine the: -3 -4 -5 2.1.1 Minor of element 4 2.1.2 Co-factor of element -2 2.1.3 Evaluate the determinant along the elements of column 3 2.2 Find the value of *z* only from the following set of equations: 2x-y+2=-1 X-y-2=0 x+y-2-z HINT: Evaluate along elements of row 1 in ALL instances.