%3D Let X be the graph of f(x) = x2/3 given below
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Q: 1. Let f : Z6 → Z6 be such that f(a) = x2 + 3. (a) Is f a well defined function? (b) Is f…
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- Let g be defined on an interval A, and let c ∈ A. (a) Explain why g'(c) in Definition 5.2.1(Differentiability) could have been given by g'(c) = limh→0g(c + h) − g(c)/h2. Recall that if R is a relation, then we can look at the inverse relation R^ -1 ={ (y,x):(x,y) in R} . Show that for a function F: X -> Y, F ^ - 1 is a (total) function if and only if F is bijective.Find the Wronskian for the set of functions.{e−x, xe−x, (x + 3)e−x}
- Suppose g is a function continuous at c and g(c) > 0. Prove that there exists δ > 0 suchthat g(x) > 0 for all x ∈ (c − δ, c + δ).Let X be f(x) = x^(2/3) , X is a subset of R x R satisfying the given equation. Define a bijective map g : X -->R. Show that your map g is well-defined, injective,and surjective.8 Examine holomorphism for given function f(z) = |z|