Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f is a 1-1 correspondence A - B. fla = f and 1gƒ = f. (a) (b)

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A: Given:     To determine: intervals in which f(x) is decreasing

Q: c) Is the function f: -2, 2] → -4, 4 with f(x) = x – 2x bijective? %3D

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Q: 5. (a) Let f: S T be a function, and A CT and BCT be subsets. Show that (A-B) = f-1(A) - f-(B). ww

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Q: Use the graphs of f and g to evaluate g(f(2)) y (2,4) (4,3) (-2,1) f (2,-2)

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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

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A: Explanation of the answer is as follows

Q: 1.) Given the function f(x,y)= 2+y=x² find and sketch the domain of f.

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Q: Find the inverse of the relation Express your answer in terms of the new 'y'. (x+7)²+(y-6)² = 19

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Q: find functions f and g so that f ∘ g = H.

A: It is given that;  H(x)=x2+1 and; (f∘g)(x)=H(x)

Q: When F(x, y, z) = , evaluate - F( - 4, 4, – 2)

A: Given statement is When F(x, y, z) = < x², z+x,y> evaluate F(-4,4,-2)

Q: Which of the following relation is a function? a) S = {(-1,-2),(-3,4), (3,1), (-5,6)} %3D b) T =…

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Q: XI. Refer to the functions f, g, and h defined here. f(x) = 1/x, g(x) = 2 vx, and h(x) = x2 -1…

A: Using rules of functions.

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A: Given query is to find individual function.

Q: Which of the following relation is a function? a) S = {(1,–2),(–3,6), (-3,2), (-1,6) b) T = {(-2,3),…

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A: Statement: Whenever P⇒Q is false then P∧NotQ is true. As it is known that P⇒Q is false only when P…

Q: 1. Let {1,2,3} and B = {3,6,9}. Which of the following are functions from A to B? If they are not…

A: Let A=1, 2, 3 and B=3, 6, 9. To determine whether the following relation is a function.If it is not…

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A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

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A: Given: g(x)=x2-x-6 We know that for a parabola given by the equation f(x)=ax2+bx+c , the coordinates…

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