Let f: X → Y and g: Y → V be functions. Show the following: (a) f is injective 3h : Y→ X such that ho f = id, (b) f is surjective 3h: Y→X such that fo h = idy Use: v injective if x1 xn → v(x1) ‡ v(xn) # How to prove these Ihs) Can you explain id x How to proof with the arrows (do you prove both rhs and

Q: Suppose f:R→IR is a diffexetiuble function which satısfies flo) = 0 . We wort to shouw f': IR → IR…

A: We have to do implicit differentiation.

Q: 5) Let f be differentiable at a. Show that f(z) is differentiable at a if and only if f' (a) = 0.

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Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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Q: Let f: X→ Y and g: Y→ V be functions. Show the following: (a) fis injective 3h : Y→ X such that ho f…

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Q: Let f(x) = (Vx + b² - b)/x, b > 0. What is the domain of f? (Select all that apply.) O (-∞, ∞)…

A: f(x)=x+b2-bx The given query is to find the domain of f(x) Also, to define the function such that it…

Q: Let f: X→ Y and g: Y→ V be functions. Show the following: 3h : Y→X such that ho f = idx (a) f is…

A: Let f:X→Y and g:Y→V be functions, To Prove: (a) f is injective ⇔there exists h:Y→X such that…

Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

A: we have to evaluate the following by using greens theorem

Q: Suppose f: X→ Y, and A, B CY. Prove that (a) f¹(AUB) = f¹(A) U f¹(B).

A: Union of two sets A and B is denoted as A∪B  It contains all the elements that are either in A or in…

Q: Differentiate the given function y = cosh(In(6x*)). 1 а) О Зг? + 4 x4 1 b) O 92? 4 x4 c) O 3z2 1 3x²…

A: Given function is y=cosh(ln6x3)

Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: 3. Let f be a bounded continuous function on C and a E C. Show that f(z) dz lim 0. iz]=r (z – a)²…

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