If f: R→ [0, ∞) is a function such that f(x - 1) + f(x + 1) = √3 f(x), then prove that f(x) is periodic and find its period.

Q: Let f(x) be periodic with period 2pi and defined on [0, 2pi] as follows:f(x) = 1 if 0 ≤ x ≤ pi/2f(x)…

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Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

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Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

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Q: f (x) = -x² + 5æ, [0, 5]

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Q: Function f that is defined and differentable on all of R.  a. suppose h(x) = (x3 − 4x-1 + 5) ·…

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Q: (2) Let f(x) = ax³ + bx? + cr + d, where a, b, c, d e R and a + 0. Prove that f(x) must have a root.…

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Q: Q1: Find the fourier expension of the periodic function whose defination in one period is: 0<x<3 3…

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Q: Consider the function g defined by g(x) = x5+x3+x.  b. Find (g-1)'(3)

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Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

Q: prove that u=y3-3x²y is a harmonic function determine its harmonic conjugate and find the…

A: consider u(x,y)=y3-3x2y