The function f(x) is defined as follows: f(x) = 1 2x + b if x ≤ 1 (2x − 1)² if x>1 - Use a mathematical sound argument to find all possible constants b such that fis differentiable at x = 1.

Q: Consider the following functions. f(x) = x, g(x) - Vx- 6 Find (fo g)(x). Find the domain of (fo…

A: Given functions are fx=x2 and gx=x-6. To find: fogx and the domain of fogx. Solution: Finding fogx.…

Q: Consider the function f(x) = x13 + 9x – 4. = 0. State any theorems a. Show that the function f(x)…

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Q: Make a graph of the function f(x) = x³ – x – 1. Use the graph to estimate a zero of the function…

A: According to the given information, it is required to first graph the given function.

Q: Let f(x)=√√4x + 7. Determine ƒ-¹(x) and the the domain of f-¹(x). ƒ−¹(x) = Domain of f(x) =

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Q: 3. Find the intervals in which the function is concave up /concave down for the function f(x) = x* –…

A: Given : f(x) = x4 - 4x3

Q: Consider the function f(x) = 12x5 +30x4 - 160x³ + 7. - f(x) has inflection points at (reading from…

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Q: Consider the function f (x) = 3 – |x – 4|| a. Graph the function and verify that f(1) = f(7) b. Note…

A: The given function is f(x)=3-x-4 The function can be redefined as  f(x)=x-1,      x<47-x,…

Q: Let f (x)=x* +2x – 3.x? – 4x +4. Find: (a) the intervals on which f (x) is increasing or decreasing.

A: Given that:  f(x) = x4 + 2x3 - 3x2 -4x + 4   find intervals on which f(x) is increasing or…

Q: 12. What is the amplitude of the graph below? y 4 0 8+ 7+ 6+ 5+ 4+ 3++ -1- -3+ -4+ -5- -6+ -7+ -8+…

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Q: f(x) = x³ – 3 %3D

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