if f(a) = b then f^-1(b) = a
from given data f(7) = 4 so f^-1(4) = 7
therefore answer is 7
QUESTION 12 Consider the function f defined by the following set of ordered pairs: f =...
(f) (4 points) The set of ordered pairs of real numbers V= | 1VER is a vector space with vector addition and scalar multiplication defined by [*1 + x2 - 1] Lyı + y2 - 1 k(y - 1)+1] Verify that there exists a vector ✓ EV such that ✓ D7=@ ū = 7, for any ve V.
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2, 2), (3,7), (4,1)} G {(1,1), (2, 1) (3, 2), (3,3), (4,2)} н 3 {(1,1), (2, 3), (3, 4), (4, 2)} (i) Does F define a function f :{1,2,3,4} (ii) Does G define a function g : {1,2,3,4} (iї) Does H define a function h : {1,2,3,4} —> {1, 2, 3, 4}? (iv) For those of f, g and h that are functions, write down...
{(5,2), (4,2), (5,3)} Is the set of ordered pairs a function?
10. 10 points. - Find the domain and range f with the following ordered pairs {(-2, -3),(-4,0), (5,3), (6,2), (2, 2)}. Then find / -'() 11. 10 points. - Find the inverse function of f(x) = -3x + 6
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10, 0sy s10 and x +y28.Find the global minimum value of f(x,y) over the set A. (Hint: see example 8 in lecture 7.) (6 marks)
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10,...
b) SST=?
C) SSE=?
SSR=?
Consider the following set of ordered pairs. Complete parts a through c. х 1 2 6 5 5 40 7 у 5 a. Calculate the slope and y-intercept for these data. Ÿ= + ( X (Round to four decimal places as needed.)
10. [4] Let R be the relation on the set {0, {f}, {y}, {x,y}} defined by R= {(S, T): SUT|=2} (a) Represent the relation R as a set of ordered pairs. (b) Represent the relation R as a relational digraph.
Consider the set of ordered pairs shown below. Assuming that the regression equation is y with caret = 4.813+0.163x and the SSE=8.744, construct a 95% confidence interval for x=3. x 2 6 1 5 4 -------------------- y 6 6 5 7 3 Click the icon to view a portion of the student's t-distribution table. Calculate the upper and lower limits of the confidence interval. UCL= LCL=
For each set of ordered pairs, indicate whether it is a function. If not, briefly explain why it is not a function. (a) { (2, 2) , (2, -3) , (2, 0) } (b) { (2, 2) , (-3, 2) , (0, 2) } (c) { (2, 2) , (-3, -3), (0, 0) }
Consider the following set of ordered pairs. X 4 5 4 6 3 3 у a) Calculate the slope and y-intercept for these data. b) Calculate the total sum of squares (SST). c) Partition the sum of squares into the SSR and SSE. a) Calculate the slope and y-intercept for these data. y=-x (Round to four decimal places as needed.)