Question

2. The function f(SID) takes as an input the student ID number of a student in this room, and returns his or her full name. Is f(SID) invertible? (That is, does it have an inverse function?) If so, what would this inverse function do? If not, why not? 3. The function (SID) takes a UC Merced student's ID number, and returns his or her height, to the nearest inch. Is h(SID) invertible? If so, what would this inverse function do? If not, why not? 4. Show that the graph of the inverse of f(x) = mx +b, where mand b are constants and m is a line with slope 1/m and y-intercept -b/m. 0 , 5. For the following functions: 1) find a formula for f'(), 2) find the domain and range for f'(x), and 3) sketch the graphs y = f(x) and y = f (x) on the same axes. To find domain and range of inverse f-'), first find domain and range of f(c) and then reverse them, see Section 6.1lecture for the discussion of this principle. (a) f(1) = -VI-I (b) f(1) = (1 - 3)2, 1 <3 (c) f(1) = -2 6. Suppose that the differentialbe function y = f(x) has an inverse and that the graph off passes through the point (2,4) and has a slope of 1/3 there. Find the value of df"/dx at = 4. 7. f(x) = 3 + 3 sin x + 2 cos r. Find (S-1)(2).

Answer 1

SID - - full name 123 АВС no f(STD) a) full name - Note that, this mapping 456 - DEF is lol & onto ( every 789 - G H I distinct SID has distinct name and for each name there is pre assigned SID. = f(SID) is invertible => it's inverse function is f'(SEN) - SIDI IWhere SEN - student's 1 full nome. omes . > => h(SID) → student's height. Here, any two student's may have some height. inverse flomation mapping may not be function. inverse mapping is not available here. 40 f(x)= murb let y = my tb -> y= b = mu => x = 4 m bom je, slope f y intercept = f'oluwa

5. (a) f(x)= -√1-1 let y=-J1-7 » 9²= 1-47 x= 1-y2 flex)= 1-22 | Domain | Range ☆ Feues |(-0,1] ( oj o to plea)(-0,00) (-0,1] F (b) f(x) = (2-3)?, *33 - det y = (2-3) 2 + + 5y = 4-3 => x= 3 I Jy => [flix) = 3157] Domain I Range fam) (-0, 3] / [0,60) o z g u fu [0,0)/(-00,00) (o fom= 2 1 let y = 2 r » *1 = 2 24-1 게시 dlo Domain 10 (1,) **) -0,0) 010,00) 12/2015)