3. Let f: AB and g: BC be invertible functions. Prove that (gof): A+C is invertible and (gof)-¹=f-¹ og ¹.

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A: We apply the vector rule.

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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Q: If f(x) ≤ g(x) for all x in [a, +∞o) and converges. •+∞ f(x) da converges, then [*** g(x) dx also

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Q: Q2/ Find the slope of the tangent to the curve at x = 8 4 + पड़े V y = 3x5 + 2³√x + 2 + √5 XY, 1-1-M…

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Q: 2n+1 (2n-3 a.) = {(2²1 =3) "" } 116) (6.) = ( ³ + 05/(1+x)} 2n+5 11a) {a}={ O {c} = √√nº +3² +1 2n²…

A: Given: 11 a) an=2n-32n+52n+1, b) bn=3+cos3n+πn and c) cn=n6+3n2+12n2+3 To determine: Whether the…

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Q: See Handout 14. Let f(x) be a function of period 2 , where f(x) = 4x for 0<x< π and f(x)=0 for…

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Q: Using Binomial theorem to find the first five terms in the expansion of the function: 1 _f(x)= 38-x²

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A: To prove the given statement we will use the method of mathematical induction in which first we…

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A: Given differential equation is x ˙= xx-1x+22

Q: Advanced Math proof? Theorem 7.3. Let T be a linear operator on a finite-dimensional vector space V…

A: We prove this theorem by using contradiction on Si for some i= 1,2,3,....,k.

Q: 1. Consider the system of linear equations below: 5x-4y+2z=21 -x-5y+6z=-24 -x-4y+5z=-21 a. Solve the…

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Q: Q 1. (a) Let R, the set of real numbers, be the universal set, A = (-3,6], B = [4, 8) and C = [2,…

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Q: 3.1 Show that a finite intersection of closed sets is closed.

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Q: 1. A₁-[0,4], A2-[1,5), A3= [0.5,3], A4- (1,9] As 2. A₁-[0,4], A₂-[1,5), A3- [0.5,3], A- (1,9] As 3.…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: nk 2j ΣΣΣ k=4j-7h=6 = I || first step 2nd step 3rd step 4th step final CTLSWET

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Q: = e-2x sin2x, y(0) = 1,

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A: Follow the steps.

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A: As per our guidelines only first three questions are solved. For remaining questions kindly repost…