1. Find constants a and b such that g(x) is continuous for all x, where if x<-1 g(x) = if if x³ ax + b (x²+2 -1

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Let if a < - 5 if -5 < x < – 1 3 if -1<x < 3 f(x) = if a 3 and g(2) = / r(e)dt Determine the value…

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

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

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Q: 3. Let f(x) = x - r - 3x. Determine the interval(s) on which f(x) is increasing and the interval(s)…

A: To find the points of minima and maxima first we need to find the critical points of function by…

Q: - If x² - x f(x) g(x) = x and X - 1 is it true that f = g?

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Q: Find values of x, if any, at which the given function is not continuous. (a) f(x) (b) f(x) = |x³ -…

A: Find the x values where the function is not continuous.

Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: Find functions g and h such that f(x) = g(h(x)). f(x) = e4x + 2 A. g(x) = 4x+2, h(x) = ex OB. g(x)=…

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Q: If the point A (4,3) and B(x,5) are on the circle with centre O (2,3). Find the Value of x

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Q: The critical point of the function f(x) = x³ – x? + 2x - 23 is (3,2) (금, -2) (음, -2) (금,2) |

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Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c…

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Q: Let f(x) = and g(x) = 2х -1 Compute (f o g)(x) and determine the domain in x-2 interval notation.

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Q: Find the value of a and b such that the function g(x) is continuous. x 3

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Q: Q.1 Find all values of x, at which f is continuous and discontinuous. x²-9 f(x) = x-3

A: 1. Given function is, f(x)=x2-9x-3=(x+3)(x-3)(x-3)=x+3 As, the function is a polynomial function and…

Q: If (2 e)(1-3e-38) f(t) = C-¹ · L-₁ { (2²-0") (1 3e-1)} is continuous for t≥ 0, find f(1), f(2), and…

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Q: Find the absolute minimums and maximums of the following function on the given intervals

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Q: Discuss the monotonicity of g (x), where g(x) = 2f + f(6-x) for all x e R. 2

A: Test for monotonicity:           let us consider a function is continuous on [a ,b] and it is…