Define the following with an example:  Domain of a function  One – to – one function  A function f is defined on the det of real numbers by Write down the domain of f.  Show that f is a one – to – one function.  Find the inverse of the function f.  Given the function f(x) = x2 , g(x) = 3x – 4, find the composite function (where means followed by g)  d) A function f is defined on the set N of natural numbers by 4 1 ( ) 2 3 x f x x + = - 1 g f - ! 1 g f - ! 1 (0) = 2, f(2) = 5 and f(n) = 2 f(n - 1) + 3 f(n - 2) + f(n - 3) for all n ³ 3

Q: 3 By using and only using function composition, show that the following function is its own inverse.…

A: The objective is to use function composition to so that the function is its own inverse.

Q: Find the entire domain on which the function f is one-to-one and non- decreasing. Write the domain…

A: f(x) = (x+3)2 so, f'(x)= 2(x+3)for f'(x)⩾ 0  ⇒ 2(x+3)⩾0                       ⇒ x ⩾ -3Hence,…

Q: Sketch a function that is one-to-one and positive for x Ú 0. Make a rough sketch of its inverse

A: If we take function fx=x2 on the interval [0,∞). This function is one to one and positive on the…

Q: verse

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Q: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B.…

A: givenA = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B

Q: If the function is one-to-one, find its inverse. If not, write "not one-to-one." 12) f(x)= 2 X-5 A)…

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Q: 7) Construct a table of values for the function f(x) = x 1 in the restricted domain (0, 0.5, 1, 1.5,…

A: Or

Q: Does the following set represent a function? R = { (0,0), (1, -1), (1,1), (3,-1), (3,3) } What is…

A: Here we use the concept of functions.

Q: Determine whether the given statement is true or false. If the statement is false, make the…

A: To determine: The given statement is true or false,  "Prove that if f and g are even functions, then…

Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

Q: Suppose the rule of the function f is "add one" and the rule of the function g is "multiply by 8."…

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Q: Let f be a function. If f (a) = f (6), then a = b. O True O False

A: We have to check is true or not

Q: Let f and g be the functions, their product and quotient are denoted by ____________ and

A:

Q: HIverse lu ..... 4IDIGGO. O A. O B. C. O D.

A:

Q: 4x+1 A function f is defined on the det of real numbers by f(x)=- 2х-3 i) Write down the domain of…

A:

Q: The domain of a one-to-one function g is [0, 15] , and its range is (0, 8). State the domain and the…

A: The domain of a one-to-one function g is 0, 15 and its range is 0, 8.