Suppose g is an odd function and let h = f ° g . Is h always an odd function? What if f  is odd? What if f is even?

Q: Either prove the following statement is true or provide an example to illustrate it is not true: if…

A: This question can be solved using the concept of even function.

Q: 121. If f(x) = a", show that f(ax) = [f(x)]“. Problems 122 and 123 provide definitions for two other…

A: Given:  f(x) = axTo Show:  f(αx) = [f(x)]αProofFirst of all Replace x by αx in the f(x) , so we get…

Q: ] Are the following functions, which are assumed to be periodic, even, odd, or neither even nor odd?…

A: We have to check whether the functions are even, odd, or periodic or not.

Q: Differentiate the following function 3 - 1 f(x) = sin (x).

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Q: The domain of the function f(x) = cos¯'( - 10) k is [A,121], Then A +k =.. Answer:

A: Since we have given that f x =cos-1 xk-10 and the domain of the given function is A, 121 To Find:…

Q: Consider the function if a € Q f(r) = if r ¢ Q. Prove that f'(0) = 0. Hint: The fact stated in…

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Q: Question 3 Given F(x) = VVx – 1, find functions f, g,h such that F = f °go h.

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Q: f(x) = tan¬1x f(x) = e* f(x) = In x 1 f(«) = !

A: Given function: fx=tan-1x Graph of the function fx=tan-1x is given below: Domain: -∞,∞ Range:…

Q: Consider the function if x E Q -x? if x ¢ Q. f(x) = Prove that f'(0) = 0. Hint: The fact stated in…

A: The given function is f(x)=x2  if x∈ℚ-x2 if x∉ℚ We have to find the derivative of function at x=0.…

Q: .Suppose f E S(R) is an even function. Show that f is also even and that

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Q: Question 2 Consider the following function f (x) = |2 – x| - |x – 4| On which of the intervals is…

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Q: Question 4 Let f(x) be a function and be R. f is continuous at x = b if and only if : 4.1 4.2 4.3

A: Given fx be a function and b∈R. We have to write the "if and only if" conditions which imply fx is…

Q: QUESTION 1 Determine the symmetry of the function. f(x): to x² + 2 O Even О odd O Neither О Both

A: If f(-x)=f(x), even If f(-x)=-f(x), odd

Q: Question 16: Determine if the function 1 f(x) = x* + x² + is even, odd, or neither. Show work.

A: The given function is,

Q: Consider the function if x e Q f(x) %3D if a ¢ Q. Prove that f'(0) = 0. Hint: The fact stated in…

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Q: Question (1): Find the interval(s) for the function f(x) = x3 – 4x² + 5x where f is concave down,…

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Q: At the point shown on the function above, which of the following is true? Of' > 0, f'' > 0 Of' > 0,…

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Q: 1. Suppose f e S(R) is an even function. Show that f is also even and that = f. (That is, f(€) →…

A: Given f∈S(R) is an even function.

Q: Only a portion of the graph of f(x) is shown below, but you can assume that f(x) is a continuous…

A: When curve below x axis then integral is always give negative values for that region

Q: Find a formula for the function f(x) such that f′(x)=tan(x)/x and f(5)=5.

A: To calculate the formula for the function f(x), where the derivative of the function is defined as…

Q: The following figure shows the graph of the derivative f`of a function f, where f is continuous on…

A: From the graph,  y=f'x For 0≤x≤2⇒f'x>0⇒fx is increasing2≤x≤4⇒f'x<0⇒fx is decreasingTake, 0≤x≤2…

Q: Suppose f ) = 4 and f' () = - = cos(x) f(x) ()- -2 and let g (x) Find g' 3 3 O 1-2/3 16 O 1+2/3 16 O…

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Q: If J is an odd function and g is an even function, then what type of function is f+g? 1S O odd O…

A: The function y=f(x) is even, if f(-x)=f(x). The function y=f(x) is odd, if f(-x)=-f(x). The constant…

Q: Which of the following theorems does not require the differentiability of the given function? a.…

A: We can check in which theorem , the condition of differentiability of the given function does not…

Q: Suppose that f (x), g(x), and h(x) are functions such that f (x) is Θ(g(x)) and g(x) is Θ(h(x)).…

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Q: Suppose that f:R → R is a continuous odd function, such that 1 f(x) dx = 5 and -1 | f(x) f(x) dx =…

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Q: Suppose g  is an odd function and let h=fog . Is h alwaysan odd function? What if f is odd? What if…

A: We know that a function is an odd function, if F(-x) =-F(x) and is an even function if F(-x)=F(x).…

Q: Draw the graph of the function f (x) = cos (2x), for the values ​​of x assigned in the following…

A: x                       f(x)=cos(2x) π·0=0 1 π4=0.7853 0 π2=1.5707…

Q: The function f is constant on I if ________.

A: To determine when the function f is constant on I.

Q: A function f is defined by if r< 0, f(2) : |r², if 20. a) State the domain of f. b) At what points…

A: The function f is defined by                           For (a), Here, the function is defined for…

Q: Question 6 Given the function f(x) = - 5 + 3x², calculate the following values: %3D f(a) = f(a + h)…

A: For f(a) ,we put x=a in f(x)  For f(a+h), we put x=a+h in f(x)

Q: The domain of the function f(x)= tanh( x - 10) is Select one: O[-10, 10] O(0, ) None OR-{10} O [ 10,…

A: Set of values of x for which function is well defined is called domain of the function

Q: Given the functions Ax) = 3* and g(x) - cos X determine the range of the function h(x) - {x) – g(x)

A: The given problem is to find the range of function h(x) = f(x) - g(x) Given f(x) = 3x and g(x)=…

Q: g are the functions whose graphs are shown, let u(x)

A: The given function is, v(x)=f(x)g(x) Then, by the quotient rule the value of v'(5) is,…

Q: Show whether the following function is continuously differentiable: f(x,y)=x3 +y3

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Q: the function is called periodic function if F(x+t) =f(x), ulgn O ihi O

A: The objective is to determine whether the statement, " The function is called periodic function if…

Q: 7. Sketch the reciprocal of each of the following functions. Ensure that if each function and its…

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Q: Question (1): Find the interval(s) for the function f(x) = x3 - 4x2 + 5x where f is concave down,…

A: Given f(x) = x3-4x2+5xf'(x) = ddxx3-4x2+5x= 3x2-8xf''(x) = ddxf'(x)= ddx3x2-8x= 6x-8

Q: It is known that f(1) = 2, f'(1) = -1, g(1) = 0, and g'(1) = 1. If F(x) = f(x) cos cos (g(x) ), then…

A: Given that f1=2, f'1=−1, g1=0 and g'1=1 And given function is Fx=fx⋅coscosgx. We have to find the…

Q: Consider the function if a €Q -22 if r ¢ Q. f(x) = Prove that f'(0) = 0. Hint: The fact stated in…

A: We will prove the result

Q: If you write the function h(x) = tan(2x) in the form h(x) = f(g(x)). then what is the function g(x)?…

A: Given ,  If we write the function h(x) = tan(2x) in the form h(x) = f(g(x))  We have to write the…

Q: On the graph of f(x)=cosx and the domain −2π≤x<0, for which of the following intervals is f(x)…

A: The given function is: f(x)=cos x ;         -2π≤x&lt;0

Q: 1. In items a through c, do the following: (i) Sketch the graph of the function; (ii) determine if f…

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Q: Suppose h = fog. Find h'(0) given that f(0) = 7, f'(3) = -1, g(0) = 3, and g'(0) = 8. h'(0) = 24

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Q: Question 4 f (x) = = +1 is an odd function. O True False

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Q: o f(x) f(x) is not a function because when x < 0 f(0) is undefined < 0 is undefined is defined

A: We have to complete the sentence.

Q: Consider the function if a € Q f(r) = ? if r ¢ Q. Prove that f'(0) = 0. Hint: The fact stated in…

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Q: Consider the functions f: [7] to [9].  How many of these functions have a range of {5,6}?

A: Given the functions f: [7] to [9]. and range of the function is {5,6}.

Q: Consider the function if a € Q f(x) = -x if r ¢ Q. Prove that f'(0) = 0. Hint: The fact stated in…

A: Topic- application of derivatives