(a) Give an example of two functions f: A→B and g: B-C such that f is both 1-1 and onto but gof is neither 1-1 nor onto (note: g of means g compose f). You may choose the sets A, B, C as you wish. (It is a good strategy to choose them as simple as possible.) (b) Given two functions f: A→B and g: B-C where ƒ and g are both onto. Prove that go also onto. of is

Q: Let f (x) + 4. Evaluate f (-8). 2 (2 f(-8) = Number

A:

Q: Let m(x) = 2x² - ax - 2 and n(x) = bx² + 2x + 5. The functions are combined to form the new function…

A:

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove that the relationship is…

A:

Q: 1 2 7 12 3 3 3 15 3 4 7 1 9

A: Recall that a relation f (also called correspondence or rule) from a set of objects A to another set…

Q: 19. Evaluate the difference quoatient: f(x+h)-f(x) h as much as possible: a.) f(x) = 2x + 7, b.)…

A:

Q: Find functions f and g so that fo g=H. H(x) =x +4 Choose the correct pair of functions. OA. OB. f(x)…

A: Solution

Q: Let g be the function g(x)=x²-x. Find g(-a). O None of these. O-a² + a O a² +1 O-a²-a O a² + a O…

A:

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f(C) -…

A:

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: Let f and g be defined by the following table:

A: We have the given table :       x  f(x) g(x) -2 6 0 -1 3 4 0 -1 1 1 -4 -3 2 0 -6…

Q: Given the function ƒ, evaluate ƒ(−1), ƒ (0), ƒ (2), and ƒ (4). ƒ(−1) = Number f(x)= { x²-1 4+x-6| if…

A: The given function is

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: Find a → evaluation for the function (4n+1) 8¹ogn

A: Solution: f(n) = (4n + 1)8log n        = (4n + 1) (23)log n              [here , we assume base of…

Q: The function f and g are defined as follows. A. -3 or f(x)%= In(x+1), x>-1 8(x)=x² +2x , x>-1 B. -3…

A: Solved below