Use the figure below to calculate each of the following. Give an exact answer. (2.1, 5.3) (2,5) (a) Let k(x) = (f(x))-¹. k '(2): = (b) Let g(x) = f-¹(x). g'(5) = f(x)

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A: Explanation of the answer is as follows

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A: Consider the given function.

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A: Let's Solve,

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A: Given f(x)=-3x+1x-3

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A: Given that hx =fgxTo find : h'-1Solution hx =fgxh'x =f'gx×g'xx=-1h'-1 =f'g-1×g'-1h'-1 =f'-2×2h'-1…

Q: Use the values in the table below to answer each of the following: f(x) g(x) f'(x) g'(x) 5 1 -1 -3…

A: Table

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Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

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Q: Given f (9) = 2, f' (9) = 6, g (9) = -1, and g' (9) = 8, find the values of the following. (a) (b)…

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Q: let (X)> and fre)=2, f ( X) is

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Q: 3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x)…

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A: Given f(x) = x + ln(x)Value of function at x = 2ef(2e) = 2e + ln(2e) = 2e+1+ln2

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A: We are asked about the derivative of the function h given a graph of the functions f and g. Note…

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Q: 2. 3 Determine f'(x) and simplify. f(x) = (3x² - 4x) (2x - 3) ³

A: Topic = Derivative

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Q: (a) Let h(x) = f(x)/g(x). Find h'(1). (b) Let h(x) = g(f(x)). Find h'(-1).

A: Definition used -           Quotient rule of derivative -…

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A: Given Function f( x ) as follows

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Q: 10. If f(x) = 2x³ - 3 x3, then f'(1) is which of the following? (B) -3 (C) -15 (E) 7 (A) 15 (D) -1

A: given function is