SPRING 2014 MATH 131 503 QUIZ 2 SOLUTION Problem 1 Given f x 4 x and g x x2 4 find f g f g f g and f g and state their domains Solution We know that f x 4 x and domain of f x say A is A 4 and g x x2 4 domain of g x say B is B 2 2 i f x g x 4 x x2 4 Domain 2 2 4 ii f x g x 4 x x2 4 Domain 2 2 4 p iii f x g x 4 x x2 4 4 x x2 4 Domain 2 2 4 f x 4 x iv In the above Domain we can t take x 6 2 and x 6 2 g x x2 4 Domain 2 2 4 Problem 2 Use the table to evaluate each expression a f g 1 b g f 1 c f f 1 x f x g x e g f 3 d g g 1 1 2 3 4 3 1 4 2 6 3 2 1 5 6 2 5 2 3 Solution a f g 1 from the table g 1 6 f g 1 f 6 5 b g f 1 f 1 3 g f 1 g 3 2 c f f 1 f 1 3 f f 1 f 3 4 d g g 1 g 1 6 g g 1 g 6 3 e g f 3 g f 3 g f 3 g 4 1 Problem 3 Determine whether f x is even odd or neither f x 1 e1 x 1 e1 x Solution To determine the given function is even or odd we use the definition i e if f x f x then f x is even in another case if f x f x then f x is odd Quiz 2 Solution f x f x We know that e x 1 e1 x 1 e1 x 1 e1 x 1 e 1 x 1 e1 x 1 e 1 x 1 1 e 1 x 1 x x e e 1 f x 1 f x 1 e1 x 1 e1 x e1 x 1 e1 x e1 x 1 e1 x e1 x e1 x e1 x e1 x 1 e1 x 1 e1 x 1 e1 x e1 x 1 f x e1 x 1 1 e1 x the given function f x is odd Problem 4 The table gives the population of the USA in millions for the years 1900 2000 Use the graphing calculator with exponential regression capability to model the US population since 1900 Use the model to estimate the population in 2014 and predict the population in 2050 Year Population 1900 76 1910 92 1920 106 1930 123 1940 131 1950 150 Year Population 1960 179 1970 203 1980 227 1990 250 2000 281 Solution The instructions for the Exponential Regression is same as in the printout given for the Linear Regression Please see eCampus for the pdf copy of the instructions about Linear Regression The only place it differs is when you are in CALC instead of LinReg scroll down and select ExpReg except this all the other steps remains the same Population in 2014 347 11 Millions Population in 2050 551 29 Millions 2 Spring 2014 c MSM
View Full Document
Unlocking...