Homework Answers
The correct answer is one-to-one function
Explanation:- Only one-to-one function have inverses. A function denotes a relationship between two or more variables and the dependent variable also known as the output variable relies upon the values of the independent variable also called input variable. In a one to one function, each output corresponds to only one input. Thus a one to one function never takes on the same value more than once.
Decide whether or not the functions are inverses of each other.Use the definition of inverses to...
Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. 44) f(x) = 1+X g(x) = 1 X-1 X A) No B) Yes
O GRAPHS AND FUNCTIONS Determining whether two functions are inverses of each other For each pair...
O GRAPHS AND FUNCTIONS Determining whether two functions are inverses of each other For each pair of functions f and g below, find f(g(x)) and g(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) X x - 3 = (b) f(x) 6 2 g(x) = 6x =...
State the 5 reasons why the inverses of the 6 trig functions are chosen in the...
State the 5 reasons why the inverses of the 6 trig functions are chosen in the way they are." For example, why is -pi/2 to pi/2 chosen for the inverse sin function. There are many other sections of the inverse sin graph that could have been chosen, so why this one? Each of these reasons is explained in words. Do not separate and address the 6 trig inverses. You are looking at the whole picture. In fact, one or more...
Use the definition of inverses to determine whether fand g are inverses. 1 f(x) = -5x...
Use the definition of inverses to determine whether fand g are inverses. 1 f(x) = -5x + 9, g(x)= x-9 Are the given functions inverses? Ο Νο Yes
Find f(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses...
Find f(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x) = 9x +3 and g(x)= a. f(g(x)) = b. gcf(x) = (Simplify your answer.) (Simplify your answer.) o f and g are inverses of each other. fand g are not inverses of each other. O
Determine whether the two functions are inverses. f(x) = , and g(x) = 4* © Yes...
Determine whether the two functions are inverses. f(x) = , and g(x) = 4* © Yes No
Use the composition of functions to determine if f(x) and g(x) are inverses of one another....
Use the composition of functions to determine if f(x) and g(x) are inverses of one another. 12. f(x) = 7x - 1 ; g(x) = x - 1
7. Determine if the two functions f and g are inverses of each other algebraically. If...
7. Determine if the two functions f and g are inverses of each other algebraically. If not, why not? X-1 X + 3 f(x) = g(x) = X-3 X + 1 0 Yes 1 No, o g)(x) = X 1 No. (fog)(x) = X
6.7.4 EXERCISE Which elements in Zio have multiplicative inverses? Which elements in Z12 have mul- tiplicative...
6.7.4 EXERCISE Which elements in Zio have multiplicative inverses? Which elements in Z12 have mul- tiplicative inverses? Which elements in Z7 have multiplicative inverses?
5a. Show that in Zp, p prime, the only elements that are self-inverses (ie. elements [a]...
5a. Show that in Zp, p prime, the only elements that are self-inverses (ie. elements [a] such that [a]. [a] = [1]) are [1] and [p 1 b. In Zp, p prime, show that [p-1)!] [-1]. This result is known as Wilson's Theorem. c. Show that if n is a positive integer greater than 1 and [(n-1)!] = [-1] in Zn, then n is prime. This is the converse of Wilson's Theorem.
Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. 44) f(x) = 1+X g(x) = 1 X-1 X A) No B) Yes
O GRAPHS AND FUNCTIONS Determining whether two functions are inverses of each other For each pair of functions f and g below, find f(g(x)) and g(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) X x - 3 = (b) f(x) 6 2 g(x) = 6x =...
Use the definition of inverses to determine whether fand g are inverses. 1 f(x) = -5x + 9, g(x)= x-9 Are the given functions inverses? Ο Νο Yes
Find f(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x) = 9x +3 and g(x)= a. f(g(x)) = b. gcf(x) = (Simplify your answer.) (Simplify your answer.) o f and g are inverses of each other. fand g are not inverses of each other. O
Determine whether the two functions are inverses. f(x) = , and g(x) = 4* © Yes No
Use the composition of functions to determine if f(x) and g(x) are inverses of one another. 12. f(x) = 7x - 1 ; g(x) = x - 1
7. Determine if the two functions f and g are inverses of each other algebraically. If not, why not? X-1 X + 3 f(x) = g(x) = X-3 X + 1 0 Yes 1 No, o g)(x) = X 1 No. (fog)(x) = X
6.7.4 EXERCISE Which elements in Zio have multiplicative inverses? Which elements in Z12 have mul- tiplicative inverses? Which elements in Z7 have multiplicative inverses?
5a. Show that in Zp, p prime, the only elements that are self-inverses (ie. elements [a] such that [a]. [a] = [1]) are [1] and [p 1 b. In Zp, p prime, show that [p-1)!] [-1]. This result is known as Wilson's Theorem. c. Show that if n is a positive integer greater than 1 and [(n-1)!] = [-1] in Zn, then n is prime. This is the converse of Wilson's Theorem.
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