The derivative of a function is given f'(z) = (2²-21-8)g(x) for some unspecified function g such that g(z) > 0 for all z: At which point(s) does f have a local minimum? 1. local minimum at x = 4 2. local minimum at x = -4 3. local minimum at x = -2 4. local minimum at r = -2, 4 5. local minimum at z = 2

Q: Suppose that the functions g and h are defined for all real numbers x as follows. g(x) = 3x+4…

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Q: f(x) = x2 + 1 and g(x) = x - 3, find (a) (f + g)(x), (b) (f - g)(x), (c) (f * g)(x), (d) (f/g)(x),…

A: We have to find domain of function

Q: For each pair of functions f(x) and g(x), find the following. P(x) = x²³² +6; g(x) = = (a) f(g(x))…

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Q: Given f(x) = 23 10x, evaluate the following. (a) (f of-)(42) = (b) (f o f)(40) = %3D

A: First we will calculate the inverse of f. Then see that the composition of f and f inverse works…

Q: write down the power seires for (x)(f(x))

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Q: If f(x) = x + 8 and g(x) = x - 8, (a) f(g(x)) %3D (b) g(f(x)): %3D (c) Thus g(x) is called an…

A: Given,           fx=x+8           gx=x-8

Q: For each pair of functions f(x) and g(x), find the following. F(x) = x³ +6; g(x) = = (a) f(g(x))…

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Q: (a) ( (b)( (c) ( (d) ( ) satisfies g(x). ) satisfies g(x). ) satisfies g(-3x). ) satisfies -g(3x).

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Q: If f(x) = x + 7 and g(æ) = x - 7, %3D %3D (a) f(g(x)) %3D (b) g(f(x)) = (c) Thus g(x) is called an…

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Q: Evaluate each of the following expressions using the given table of values 2 (a) f(g(-1)) 1 2 (a)…

A: x-2-1012f(x)-10-21-1g(x)210-10The values of different functions at different inputs are given

Q: If f(x) = x + 6 and g(x) = x² - 5, find the following. b. g(f(0)) d. g(f(x)) a. f(g(0)) c. f(g(x))

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

Q: Consider two functions f(x) and g(x), and such that fˆ−1 (x) = g(x) Must it also be true that…

A: To explain that if f-1x=gx then g-1x=fx is true or not.

Q: Show that E( X - K )2 = var( X) + [E(X) - K]2

A: var(X)=E(X2)-E(X)2 E(a)=a  where a is constant (a-b)2=a2-2ab+b2

Q: If g (x)= x+3 -. find g(g(g(1))). and g(g(g(g(1))). g(g(g(1))) =| g(g(g(g(1))) =

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Q: Suppose f(x) = x2 + 1  and g(x) = x + 1    Then (f + g)(x) = (f - g)(x) = (f/g)(x) = (f ∘ g)(x) =…

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Q: if g(x) = (1/5)xfind g(-2)

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Q: (-9)" (2n)! n=0 (a)e³ (b) cos 3 (c) co (d) sin 3 (e) None

A: The given series is ∑n=0∞(-9)n(2n)!