2. Consider f: R→ R with f(x) = x rational x irrational Show that f is discontinuous at every real number.

Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

A:

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: Let f(x) = (x²-8x+6 (4x+9 for x ≤6 for x > 6 Find the value of f(7). A. 34 C. - 7 Select one: Ο Α O…

A: To find the value of f(7), we need to determine which part of the piecewise function to use. Since…

Q: If f is analytic in a neighborhood of ro and f(xo) = 0, show that f(r)/(x – ro) is analytic in the…

A: Analyticity

Q: Define the following real function: f(x) = 2 - x, x is rational and f(x) x2, x is irrational. What…

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Q: (c) Show that f(x)>0 for all values of x, x # -2.

A:

Q: Let f (x) = x2 if x is rational and f (x) = 0 if x is irrational. b) Prove that f is differentiable…

A: Given fx=x2x is rational0x is irrational To prove f is differentiable at exactly one point, namely…

Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: The domain of the function f(x) = arccos(√3x²-2) is: O A. all x in the interval [¹]. O B. all x in…

A: we need to find the domain of the given function.

Q: ( x2, if x is rational Define the function f: R → IR by f (x) = -x², if x is irrational. At what…

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Q: 호호 -^ z-vz44 Z

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Q: 4. Let f(x) := r³ – 15x + 1. (a) Use the Intermediate Value Theorem to prove that f(x) has a root on…

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Q: Is the function f: R → R defined by is f(x) = x² + 3x − 2 injective? Show clearly why or why

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