
mocr.marico Which of the following have inverse functions? y 3 2 + 4 y 3 2-...
5. Which is the graph of the following parametric equation? (1 point) 2 x-E and y 2-3 .y t-4 5 t-4 3- 2- 3- 2- 5 -4 -3 -2 10 -1 2 3 4 t-1 t=0 it 6: Parametric Functions 6 3 2- 1- -5-4-3-2-1.0 -1 -2 -3 t 0 2- t= 16 2 4 -3 2 1 12 3 4 5 -1 1 -2 -4 ametric Functions Test 6: Parametric Functions t 16 1- 1/2 3 4 5 -1...
Random variables X and Y have following distributions: PIX = -4) = 2/3, P(X = -1) = 1/3 PſY = 2) = 1/2, P(Y = 3) = 1/2 a) (5 points) Using the moment generating functions for the random variables above find: E[X+Y] b) (5 points) Using the moment generating functions for the random variables above find: Var(X+Y)
4. Solve the following system of linear equations using the inverse matrix method. 1 y = 1 2 , 3 2 -r- 1 5 4 a) x+y +z= 6 x-y-3z=-8 x+y- 2z=-6 b) Solve the following system of linear equations using Cramer's Rule. 5. 2 1 -X- 3 2 1 3 X+-y-1 5 4 y = 1 a) x+y+z= 6 x-y-3z=-8 x+y- 2z = -6 b)
4. Solve the following system of linear equations using the inverse matrix method. 1...
Explain relationships and properties between inverse functions 1. Consider how Alex, Jordan and Kelly found the inverse function of f(x) = Alex's work Jordan's work y = ²X+1 foftly) f(x)= y x + 1 ore So: x=2/34 +1 x-1= 234 V - y I f(f="(y)) = 2 / 3 f (y) + 1 = y 2/3f-lly)=4-1 (y) (y) Kelly's work 6 y = 2x + 1 9-1= 2x 3(4-1) = 2x 3(4-1) = x 2 But f(x) y f"(f(x) =...
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1) Property of inverse functions If f(x): (-1,4 ] → [3,7) → this means f(x) is a function with domain (-1,4 ) and range (3,7] And f(x) is known to have an inverse function; f(x) Find the domain and range of f(x) f-1(x): HINT: x by y's 2. Inverse functions of well known functions – find the inverse function-use proper notation - an inverse function is not a single sided express if f(x) =x, the inverse function...
O GRAPHS AND FUNCTIONS Inverse functions: Linear, discrete The one-to-one functions g and h are defined as follows. g={(-2, 5), (3, - 2), (6, 4), (8, 9)} h(x)= *+9 11 Find the following. 8'(-2) = 0 00 x X 5 ? (non ') (1) = 0
Random variables X and Y have following distributions. PIX = -1) = 3/4, PIX = -2) = 1/4 PIY = 3) = 1/2, P(Y = 2) = 1/2 a) Using the moment generating functions for random variables above find: E[X +Y] b) Using the moment generating functions for random variables above find: Var(X + Y)
-trix Example 1: Solve the following systems by finding the inverse of AT 13x+y = 3 ems by finding the inverse of the coefficient matrix. [21] B[] cx[j] ab 2 lil (x-2y=8 A -1 Find Al=ad.bc = 1(1) - 1(2) = -1 to 2 x + y = 1 12x + y = 3 A TAL- Z1J IN X=-4+3 x -y=1 sx+y=3 TGA 16-17 -11-25 -110/= 9. x - y = 1 X = A B - 27- 177 2...
= OGRAPHS AND FUNCTIONS Inverse functions: Linear, discrete The one-to-one functions g and h are defined as follows. g(x) = 4x -9 h={(3, 5), (4, - 7), (5, 4), (8, 1), (9, 3)} Find the following. DO 8-'(x) = 0 (es)6) = 0 X Ś ?
O Graphs of inverse functions are a reflection of the original function over the y = x graph. If the original function has the points (2,7) and (-3, 8), a y-intercept of 1, and a domain of (-5,4], describe some features of its inverse function.