#7 and #13

-One function touch the x-axis? 10. Can a continuous one-to-one function have the values given below Exp why it is not possible? X f(x) | 2 3 11. The graph of f(x) = x - 2.INT(x) for -2 sx 53 is given in Fig. 11. (a) Is f a one-to-one function? (b) Is f an increasing function? a decreasing function? 12. Is every linear function f(x) = ax + b one-to-one? 13. Show that the function f(x) = In(x) is one-to-one for x > 0. 14. Show that the function f(x) = ef is one-to-one. Fig. 1 In problems 15 - 18, rules are given for encoding a 6 letter alphabet. For each proble (a) Is the encoding rule a function? (b) Is the encoding rule one-to-one? (c) (d) Write a table for decoding the encoded letters and use it to decode your answer (e) Graph the encoding rule and the decoding rule. (Fig. 12 shows the graphs for4. The values of w and w ' are given in Table 8. X W ( x ) W'( x ) |W ( x ) ( w ) ' ( x ) Complete the columns for w and ( w ) ' WNA NWA UION 5. Fig. 10 shows the graph of f. Sketch the graph of f-1 I Table 8 6. Fig. 11 shows the graph of g. Sketch y the graph of g. 7. If the graphs of f and f intersect at the point (a ,b), how are a and b related? X 8. If the graph f intersects the line y = x at x = a, does Fig. 10 the graph of f intersect y = x? If so, where? 9. The steps to evaluate the function f(x) = 7x - 5 4 are (1) multiply by 7, (2) subtract 5 , and (3) divide by 4. Write the steps, in words, for the inverse of this function, and then translate the verbal steps for the inverse into a formula for the inverse function. Fig. 11 10. Find a formula for the inverse function of f(x) = 3x -2. Verify that f-(f(5) ) =5 and f( f-1(2) ) = 2