Find the values of a and b for which g(x) is continuous for all x. -5 if x < -1 ax+b if -1 < x < 1 17 if x ≥ 1 g(x)= a= b=

Q: Find intervals where g(x) = 3x − x3 is increasing

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Q: 1. f : R → R such that f(x) = 6x + 42 2. f : Z → Z such that f(x) = 7x + 34 3. g : R → R such that…

A: Four real-valued functions are given to check their functional behavior.   NOTE: Kindly note that we…

Q: Consider the function f(x) where. 2x²-x +3. if x>2 jf x=2 if x<a f(x) = 4 4-X Is the function…

A: Solution:

Q: Match the piecewise function with its graph. (2x-1, if x-1 A) B) 8 -6 -4 -2 C) D) -4 -6 -4 E) AB) -6…

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Q: Determine the interval (s) where the following function is continuous x-7 f(x)= (x-7)x+4)

A: In the given function (x-7) is a common factor in numerator and denominator. So, it will cancel out…

Q: f(x) The quotient, denoted by 2, is the function denoted by 2(2) = g(x) excluding the values of x…

A: Given that the quotient, denoted by fg, is the function defined by fg(x)=f(x)g(x) , excluding the…

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

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Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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Q: Find the intervals on which the following function are increasing and decreasing and also locate…

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Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

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Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: (x² + 1 if x -1

A: For function g(x) to be continuous on -1 limx→-1-g(x)=limx→-1+g(x)=g(-1)…

Q: 9) Evaluate the piecewise function for x = -1 and x = 4. 2x + 1 if x 2 h(-1) = h(4) =

A: To evaluate the piecewise function for x=-1 and x=4.hx=2x+1  if x≤2x2-4  if x&gt;2h-1=?h4=?

Q: state all intervals of x where f(x) is increasing.

A: TO FIND INTERVAL WHERE f(x) is INCREASING FIND f '(x) and see interval where f '(x) &gt;0 f(x)…

Q: f (x) = x + 2x³ – x² – 2 %3D

A: Given: Determine if the given function is continuous at every real number f(x)=x4+2x3-x2-2

Q: 2. Evaluate the piecewise defined function at the indicated values. x2 + 4x if x s -3 Ax) = {x if -3…

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Q: 2x -5x+3 2. Given h(x) = x? +x-2 At what value of x does the function have an infinite…

A: Topic = Functions As per guidelines , At  a time only three sub-parts can be answered.   1) An…

Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: Suppose that 3 <f"(x) < 5 for all values of x. Show that 18 < f(8) – f(2) < 30.

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