a) Determine whether each of these functions is a bijection from R to R. i) f(x) = 2x +1 ii) f(x) = x² +1 b) Find these values D 旧+周-目+引 ii) [10.8] + [1.9] + [2.61]

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

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A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: 3. Show that the function p : F → Ę which maps o to o is a bijection from F to Fe, where and ar to…

A: Let ϕ:F1→F2 be a function such that, ϕ0=0. Also given that ϕαr=β3r, where 0≤r≤6 When r=0,…

Q: 3) By changing the independent variables x and y to u and v by means of the relations u xay, v = x +…

A: Apply chain rule

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A: See the attachment

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A: See solution below

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Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

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A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

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A: Given- x + y + z = xyz This inequality can be proved by magic no. Concept-  First we will prove…

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A: A function is injective if f(x)=f(y)⇒x=y. A function is onto if for every y in Y there exists a x in…

Q: Use the Cauchy-Riemann PDES to determine all points 2 =r+ iy €C in which the following functions are…

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A: We have to check

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Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

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A: To prove: For any x∈ℝ, x·0=0.

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A: Given that, G is the midpoint of IE¯ So IG¯=GE¯ ∠I=∠E∠1=∠2

Q: Assume f,g : [a, b] → [c, d] where a < b and c < d. Prove that sup{f(x)+g(x) : x € [a, b]} <…

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Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.