2. Let f (a, b)→ R be a function and suppose there exists constants M > 0 and a > 1 such that |f(x) = f(y)| ≤ Mx - yª for all x, y € (a, b). Prove or disprove that f is a constant function.

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

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Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: 7 (:) Prove that f(x) : is convex.

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A: Bartleby Guideline : ''Since you have posted a question with multiple sub parts , we will provide…

Q: Let f: X --> Y be a function, and let U be a subset of X.  (1) Prove or disprove that f maps X \ U…

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Q: 2. Let us define a. Verify that f(x, y) = af ду xy(x² - y²) x² + y² af y(x² - y² + 4x²y²) əx (x² +…

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Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

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Q: 3. Let f : R² → R be a strictly convex C² function and g(x) = f(x)+(x1+ 2r2)² Show that g is also a…

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