(d) Suppose that ƒ: P → Q and g: Q → R are functions. (i) Show that the composite function gof : P → R is bijective if both ƒ and g are bijective. (ii) If gof is bijective, show that (gof)−¹ = f−¹og¯¹.

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Q: Use calculus to show that the function, f (x) = x³ + 3x – 6, has exactly three zeros (where f(x) =…

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Q: Use the graphs of f and g to evaluate the function (a) ( f ∘ g)(2) (b) (g ∘ f)(2).

A: (a) f∘g2=fg2=f2=0 Hence the answer.

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…

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Q: Write out all functions f: {1,2} {a, b, c, d) (in two-line notation). How many functions are there?…

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Q: Let A = {-4, 0, 4} and B = {t, u, v, w}. Define a function F: A → B by the following arrow diagram:…

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Q: assume that f is an even function and g is an odd function. Both f and g are defined on the real…

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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…

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Q: Use the graphs of f and g to evaluate the function (a) ( f ∘ g)(1) (b) (g ∘ f )(3).

A: To evaluate the function (a) ( f ∘ g)(1). (b) (g ∘ f )(3).

Q: Let f(x) = x and g(x) = x-8. Determine the composite functionfog and its domain. %3D (fo g)(x) =…

A: given that fx=x and gx=x3-8determine the composite function fog and its domain

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) -…

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Q: Use the graphs of f and g (see attached) to evaluate the composite function :  (f ∘ g)(-1)

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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: Use the graphs of f and g (see attached) to evaluate the composite function : (g ∘ f)(0)

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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: -1| 03 f(x) | 15 8 | -1

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Q: Let g : A → B and f : B → C be functions. If f ◦ g : A → C is 1-1, then g is 1-1.(a) Prove this…

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Q: Let f: A --> B and let B1 and B2 be subsets of B. What is f-1(B1), the inverse image of B1? Prove or…

A: Given:

Q: Find the inverse of the function f:[0,9] → [1,5] , f(x) ={Vx + 1 if 0<x<8 (2x – 13 if 8 < x<9 %3D |

A: