et f: (a, b) → R. If f'(x) exists for each x, a < x

Q: If f is even, then f' is even.

A: The question is taken from the function in which we have to do that f is even then its derivative is…

Q: lim f(x, y) = f(a, b). (x,y)→(a,b) If f is a rational function, then Select one: True False

A: To find the given statements are true or not.

Q: 1 F F[f (at)] a ).

A:

Q: Prove that if f is a continuous function on a closed interval [a, b], then

A: We have to prove the given inequality for a continuous function on a closed interval [a,b].

Q: f: Z4 → Z5 f([a]4) [39]s if a > 0. =

A: Introduction: A well-defined function is a function that is unambiguously specified by its…

Q: prove that any Continuouse function [a,b] en is measurable.

A:

Q: Could you write a proof for the following: Suppose F: X → Y is one-to-one. Prove that for all…

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Q: Let 1 f(x) = ,* – 8, – 4 < x < 8 1 The domain of f¯'is the interval [A, B] where A and B = Check…

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Define f: R-&gt;R as follows: f(x)=x-[x] if [x] is even. f(x)=x-[x+1] if [x] is odd. Determine those…

A: To find the points where the given function is continuous.Take two cases:Case 1: Let x = a is an…

Q: . If f : (0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: See the detailed solution below.

Q: prove that any Continuouse function [a,b] en is measurable.

A:

Q: If f is differentiable and non-negative on an interval I in R then /3f + 1 is differentiable on I.…

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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 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: If fis a bijection, find the sets X and Y.

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Q: Suppose that f:I->R is a continuous function and that |f| is a constant function. Prove that f is a…

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