Which of the following statements is true for f(x) = (x² – 1)e-a where a is a constant? O None of the others are correct. O f(x) has no critical points for all a. O f(x) can have three critical points. O f(x) has exactly two critical points for all a. O f(x) has one or two critical points depending on the value of a. O f(x) has exactly one critical point for all a.

Q: Find all values of x in the domain F such that F’(x) does not exist. B.Find the critical numbers of…

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Q: Consider the values of f and g in the given table. |f(x) f'(x) g(x) g'(x) 1 4 |-2 |-1 2 |-3 1 2 3 1…

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Q: 1. Which of the following functions has its only zero at x = -4? O sG) = |x| +4 O sG) = | x | - 4 O…

A: zero of function when is at where function attains zero value.

Q: 4. Find three functions f, g,h that satisfy: f(g(h(x)))= +2 Vx?

A: Given,             fghx=1x2+2

Q: 6. Give four non-trivial functions f(x), g(x), h(x) and j(x) such that Vx2 – 1+5 - (f ogohoj)(x) = V…

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Q: Determine which of the following pairs of functions are linearly independent. dependent 1. f(x) = x³…

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Q: Suppose X has the following p.m.f. f(x) = cx2, x= - 1,0,1 for a constant c. A. Determine the…

A: For any probability distribution to be valid, the sum of probabilities over the range of the random…

Q: 2. Given the functions f(x) = x - 2 and g(x) = x² – 1 determine all values of x for which Ag(x)) =…

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Q: Let f(t) = (t − 1)(t − 2)(t – 3). What are all critical points of f? f has no real critical points.…

A: To find all critical points of .

Q: 7. Given f(x) = x² – 5x ,

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Q: Find the critical numbers of g(x) (Exact answers only) x2 %3D

A: The given function is gx=lnxx2

Q: a and d, please

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Q: Given that f(x) = x² – 9x and g(x) = x + 4, calculate (f o g)(x) or f(g(x))

A: Given f(x)=x2-9x and g(x)=x+4