If the function f(x) is even, which of the following is ze an O bn ao nothing is zero

Q: f is continuous iff f-1(E) is closed

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Q: Suppose f(x) = 4nx2e Ax* for all x E R. Show that f = -f. %3D -e

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Q: The following statement is false, explain why. The function g(x) = x^2 on the interval [-1,1] has…

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Q: on satisfying f'(x) the function sat

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 – 4…

A: Given f(x) = x2-4x-2x<2ax2-bx+32≤x<32x-a+bx≥3 It is continuous if and only if limx→2-f(x) =…

Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

A: Introduction :

Q: If f(0) = 0 and f"(x) exists for all x>0, then show that %3D f(x) f'(x) xf"(5), 0 < § < x. Also…

A: Let's find.

Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: 8. Given the following function f, define f(1) so that f is con- tinuous at x = 1, if possible: Зх —…

A: Given: fx=3x-1if x&lt;1x2+1if x&gt;1

Q: What is the type of the following function: f(x) = r' +5 where the domain is Z and the codomain is Z

A: Let f(x) = f(y) for two integers x and y.     =&gt; x3 + 5 = y3 + 5    =&gt; x3 = y3     =&gt; (x -…

Q: of a and b such that the following function is continuous everywhere. wer. ax² + 2bx 19 x 2

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Q: iff.g,h becontinuous functions on [0,a]such that and sh(x)-4h(a - x)=5, then provw that…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 16x – 5 on the interval [2, 6], how many…

A: Given,          fx=2x2-16x-5 on the interval 2,6.We know that,         Rolle's theorem states that…

Q: Suppose f is a twice differentiable function at every x. Suppose further that f'(3) = 0,f'(4) =…

A: If the f is twice differentiable function then if f''(a) =0 , so a is the inflection point, if…

Q: Are the following functions quasiconcave, quasiconvex, both, or neither: f(x) = x³ - 2x f(x₁, x₂) =…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: If f(x) is continuous, f(-1) = 2, and f(2)= -1, then f(x) has a root in [-1,2].

A: Given:  fx is continuous , f-1= 2, f2 = -1  To Prove:  fx has a root in -1,2

Q: Given the function y=f(x), y" is found to be negative over the interval (4,8), then over this…

A: Answer is given in next step.

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

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Q: 1) Find the values of a and b that make f continuous everywhere. x' - if x<2 х—2 f (x) = { ax? –…

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous everywhere  so…

Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

A: Given function is: hx=-x-2    ;  if x&lt;-24-x2     ;  if -2≤x&lt;2x-3  ;  if x&gt;2 We have to…

Q: ) If f(x) = (0 <* < 1) (-1 < * < 0) expand f(x) in the form c,P(x).

A: According to our company policy i am supposed to answer ony one question at a time.  For the rest…

Q: For a function g(x), if there exists x E[a,b] such that g'(x)> 1, then we conclude that g(x) has not…

A: For a function g(x), if there exists x∈[a,b] such that g'(x)&gt; 1, then we conclude that g(x) has…

Q: | if x#3 6. %3D 15. Show that if the function g is defined by g(x) = if x=3 then g is not continuous…

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Q: Suppose f(x) and f'(x) have the following values. -7 -6 -5 -4 -3 4 -9 1 9 2 6 x f(x) -2 f'(x) 1 -2 3…

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Show that the function f : N → N, given by f(x) = 2x, is one-one but not onto.

A: If f(x1) ≠ f(x2) then we get:

Q: (2) The real part of Syy (@) and the real part of Syx (@) are even functions of o, i.e., Re[Sy (@)]…

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Q: Let f: R R and let f(x) >0 for all xER. Show that f(x) is strictly increasing if and only if the…

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Q: Use an (e – 6) argument to show that f : R →R be the function defined by 2 - 5x – 5 if I >-1 2+1+1 f…

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Q: For the function f (x) = |x| defined on [-1,1], there is some -1<c<1such that f' (c) = 0. O True…

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Q: If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

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Q: A function f: Z x Z is defined as f(m, n) = 3n - 4m.  Verify whether this function is injective and…

A: f: Z x Z is defined as f(m, n) = 3n - 4m So, f(m, n) = f(a, b) implies, 3n - 4m = 3b - 4a i.e. 3(n…

Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: Suppose that f, g and g' are continuous on the interval I = {x : a <x < b}. Show that f f (x)dg(x)…

A: Given that the functions f,g and g' is a continuous function on the interval defined as  I=x:a≤x≤b…

Q: f is also constant

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Q: Let f(x) = { if x - 4 m= mx 6 - If f(x) is a function which is continuous everywhere, then we must…

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Q: Given F(X)= ×2_x+1 if ×ン Find the uaIue oFF(2) -f (o) an

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Q: xe* if x < 0 g(x) = x – 2x2 + x if 0 < x < c , .3 if x 2 c

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Q: If we apply Rolle's Theorem to the function f(x) = 2x- 16x 6 on the interval [2, 6|, how many values…

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Q: Given the function y=f(x), y" is found to be positive over the interval (4,8), then over this…

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Q: 10. Consider the function if a E Q -a? if x ¢ Q. f(x) = Prove that f'(0) = 0. %3D

A: Solution:Given  f(x)=x2if x∈Q-x2if x∉QTo prove f'(0)=0Formuladdx(xn)=nxn-1

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: Which of the following is the domain set of the function f(x.y)= arccos(x² + y² - 3)+In(x² +y² -3) ?

A: In this question, we evaluate the domain of multivariable function and in second part we check the…

Q: consider a function f:lo 11-» R. and etheruoise iff RELmaan amntegrable DY not A=3+1

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Q: If f(x) and g(x) are defined on domains A and B respectively, then the domain of f(x) + g(x) is? *

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Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 8x - 1 on the interval [0, 4], how many…

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Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: If f is increasing and f(x)>0 on,I, then g(x)=1/f(x) is decreasing on I. Select one: True False

A: Theorem Related to Increasing and Decreasing Function: Let f be a function defined on the interval…

Q: Suppose that f(z) is an entire function and there exists a c € R s.t. Re(f(z)) <c for all z Hint:…

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