Suppose f : Z → Z is defined by f(x) = 5æ – 2. O a. fis invertible and its inverse is f-' = 5x + 2. 1 I+2 O b. f is invertible and its inverse is f-! = . O c. f is not invertible because it is not one-to-one. O d. f is not invertible because it is not onto.

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Q: 0 0 0 1 0 0 0 1 0 ) Let A =

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Q: Z. F(x, у, 2) %3D y z x/

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A: As per our norms we have to write one question at a time kindly repost remaining questions.

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A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

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Q: Show that if A is invertible and DA = CA, then D = C.

A: Given that, A is invertible and DA=CA.

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Q: Exercise 3. Show that f : Z → N so that f (z) = z² + 1 for all z E Z is neither one-to-one %3D nor…

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

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Q: 8. Prove the following properties of the Fourier convolution: (a) f (x) * g (x) = g (x) * f (x), (b)…

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A: Let us start solving the problem step by step.... We need to find the z-transform of x(n)

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A: Given ut=ux, -∞&lt;x&lt;∞, t&gt;0, ux,0=-x

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Q: . Let Show that, Hence show that •2T F₁(x) = 2/1/² 0 Fn(2) = eix cos ∞ N=-∞ eix cose eine de in Jn…

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A: Given, the operator  A : L20, 1→L10, 1 defind by                               A(f)(x)=(f(x))2+f(x)…

Q: (B) Compute the discrete Fourier transform of g = t+1 on [0, 4) with length 3. F{8} = (C

A: To calculate the discrete Fourier transform of the below function on [0,4) with length 3. g=t+1

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Q: Find the Laplace transform of : F(t) : . f (s) = ( 3n)! (s+4)3n+1 2 s+4 f (s) = + 2 3n! s+4…

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Q: Compute the discrete Fourier transform of g = t + 1 on [0, 4) with length 3.

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Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: Prove that the Generating function of Bessel function i.e. £1J„(x)t" = e*/2(-1/2), %3D

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