Consider the following functions. (c) f: GL₂(R) → RX, f + ((ad)) (($)) (d) f: GL₂(R) → R, ƒ (e) f: GL₂(R) → RX, f = ab. = a + d. (i) Is f a homomorphism? (ii) Is f injective? = ad-bc. For each of these functions, answer the following questions, with a (brief) justifi- cation.

Q: 3. Determine if the following functions are one-one. Explain why. •f: R R f(x) = (x - 2)² ● f:R R…

A: one- one function :Let f be a function which is one one if        x1≠x2   ⇒  f(x1) ≠ fx2 for every…

Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

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Q: . Consider the functions f : A → B and g : B → C. a) If f and g are both injective, show that g o f.…

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Q: Let f: IR → R and g: R → R with f(x) = 5x – 7 and g(x) = x2 – 4x + 4 Find: a) Domain of . g(D(f.g))…

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Q: and (a) (b) (c) f: R² → R² (x,y) → (y,x) g: R² (x,y) → R² (x+3, y - 4). Describe the geometric…

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Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: 2. Consider the functions g, h: R → R defined by g(x) = x² and h(x) = x³ + 1. A. Evaluate f(g(x) ·…

A: g(x)=x2h(x)=x3+1∫xndx=xn+1n+1+c

Q: (b) Define a function F:F: R XR → R XR as follows: For all (x, y) ERXR, (F(x, y) = (2x + y, 2x - y)…

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Q: Let f : R → R be defined as f(x) = x3 + 8 (i) Prove that f is a bijection (one-to-one…

A: Consider the given function.

Q: 5. Consider the function f : Z × Z → Z × Z defined as f(n, m) = (n + m, 3n + 4m). (a) Find (n, m) E…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Use the graph of the function f shown to the right to find f(-1), f(0), and f(1). f(-1) =

A: Given the graph of function of f . To find f(-1) , f(0) and f(1) using the graph.

Q: Use the graph of f below to answer the following questions: (4, 2) 2 1 -4 3 -1 (-4, – 1) a) f(x) dx…

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Q: (2) Determine if given expression is a function. If so, find out if it is one to one, onto or…

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Q: 1. Define f : (- o, 2) → (- 0, 1) by f(x) = . Show that f is bijective. x+1 *-2

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Q: Which of the followings are the inflection points of f(r) = Inz I. x=0 II. x=e III. x=1 IV. ¤ = e 2…

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Q: (a) Show that the formula (VæR(g(x), x) = Vx3yR(y,x)) is universally valid, where g is a 1-place…

A: Part(a): As we know, ∀xRgx,x⇒∀x∃yRy,x Where g is a two place function symbol and R is a two place…

Q: 2. ( images. (a) f({0, 1, 2}) Let f: Z→ R, with f(n) = 4-n². Find the following direct and inverse…

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Q: Prove that the following functions are bijections: (a)  f: R → R given by f(x)=ax+b, where a ≠ 0.…

A: Let f:A->B be a function. Injective function: f is said to be injective if different elements…

Q: Show that the following relations are not functions on R. a) ƒ = {(x, y) = RxR | y=x/(x² −7x+12)}

A: Given function. y=xx2-7x+12 is not define for x2-7x+12=0 => (x-3)(x-4)=0

Q: Show that for any function f : X → Y , there are two functions g : S → T and h : X → S such that (a)…

A: To Show: Show that for any function f : X → Y, there are two functions g: S → T and h: X → S such…

Q: (a) Let f:Q → Q be the function defined as follows: f(x) = 1 + 2x. Is f(x) a surjective function?…

A: Solution

Q: u+iv is analytic function, under what condition (if any) v+iu

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Q: The function, f(x), is a 1-1 function with Dr: (-0,5] and Rf: (-4,6] U [7, 0). State the domain and…

A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: (a) Let f, 9, h : N → R²º. Prove or disprove that if f + g€ O(h), then f e O(h) and gE O(h). (b) For…

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Q: f: (R, +) → (R*, .) where f(x) = 2*

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Q: 3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R,…

A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

Q: Consider the function f: R → R defined by f(x) = x³ – 3x + 2. Then (A) ƒ is increasing on the…

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Q: What is the inverse of the function 2х + 1 f:R → R, f(x) ? 3.

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Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: d. For each of the following, state whether the functions f: R → R, x → f(x) are injective,…

A: Given functions: fx=3x+2 fx=3x3-7x+3 fx=x6 fx=sinx fx=0.01x fx=4 We have to check whether the…

Q: 4. (a) (b) Let f : X → Y and g: Y→ Z be functions. Prove the following statements. If gof is…

A: