we have f: X→Y is a 1-1 function and Y is countable. Since f is 1-1, is it correct that this implies X ~ f(X) [which is f:X →f(X)] which further implies bijecton? Also, does this imply f(X) ⊆ Y?

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: - h)? + k: a). f(x) = 2x² –12x+11; b) y = -r+x+:

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: x4 – 10 хе (-о, л — е) 2: х4 +9 хе [л— е, оо) - f(x) = Evaluate f(0)г

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Q: F. Determine the following given that 1. f(g(x)) 2. g(f(x)) 3. f(g(-1)) 4. g(f(2)) f(x)=x²+x-3 and…

A: As per our guidelines, we are supposed to answer only one question with three subparts only. since…

Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: x+7, -4 h er. f(0) = 7. f(1) = 8, f(2) = -5, and f(3) = -10, of b

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Q: Prove the validity of the following arguments Vx, A(x) → B(x) Ex, A(x) ^ C(x) Vx, C(x) →D(x) ..3x,…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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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: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

A:

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: If f(x) = x + 9 – x and g(u) = u + V9 – u, is it true that f= g? Yes No

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Q: ,x2

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Q: For the function f (x) = + 8, find f-1(x). (r-4)5 O f-1(x) = V8x – 8 + 4 O f-'(x) = /8 (x – 8) + 4…

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Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

A:

Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Define f(x ) = Vx2 +1 and g(x) = 2 – x2. State the domain of (f + g)(x ). x # v2, –v2 - [-1, 00)…

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Q: Let b be a zero of f(x) = x5 + 2x + 4 Show that none of √2, ∛2, ∜2 belongs to Q(β).

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Q: Write the domain in interval notation. 3) y (t)=√√√8-t 4) f(x) = x - 4 x-5

A:

Q: In each of the following, determine whether

A: We have to decide whether y is a function of x or not.

Q: I understand the process of proving 1-1 and onto, however, how did you obtain the function f(x) =…

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Q: Determine the domain of the following functions: За — 6 a) a(x) b) b(x) = /5 – x c) c(x) = 3x4 –…

A: We can find the domain of the given functions as below.