7. Decide if the following functions are one-to-one. Prove your answers.. (a) f(x) = x² – 1 (b) g(x) = 2x +1

Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

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Q: Find the local and absolute extremum for the functions over their domain: x²+2x-3 4. f(x) : x-2 ||

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Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: For what value of the constant c is the function f continuous on (-∞, ∞)? ( cx2 + 2x x3 - cx if x <…

A: We know that for any value of c, for x &lt; 5, the function is continuous and for x &gt;= 5, the…

Q: 14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: I. Solve the following problems on functions. 1. If g(x)= v36 - x² , find g(0), g( - 3), g(=), g(2y)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: do you agree with the contention that the functions f(x) = x+2 and g(x)=x2-4 /x-2 are the same in…

A: It is given that, f(x) = (x+2)     and     g(x) = ( x2-4)/(x-2) Then we will prove that f(x) and…

Q: 1) Find all relative extrema in the function f (x) = x 3 + 3x2 – 24x + 12.

A: For relative extrema the derivative of the function will be zero. Thus,…

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

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Q: It was determined that the number of prey consumed by a predator over a period of time was a…

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Q: Answer the following questions for the function f(x) = x/x² + 4 defined on the interval -7 < x < 5.…

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Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: (a): Find the value of k that makes function continuous at x = 4 f (x) = 7x S2x + 7 x > 4 k x < 4…

A: We will use the definition of continuity at a point to find the value of k

Q: b. For what value of (k) is the function y=f(x) continuous at x=3. x3-3x2-4x+12 x#3 x-3 f(x) = k x =…

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Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: Determine the equation of the line tangent to the graph of the following function at x = 0. g(x)…

A: The given function is

Q: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 + 2x² –…

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Q: 21. Suppose f(x) = A and g(x) = v2*. Find the x-value for which the two functions are equal.

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Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: The function h(x) 1 can be expressed in the form f(g(æ)), wher x + 4 defined as: f(x) =

A: The function h(x)=1x+4 can be expressed in the form f(g(x)), where g(x)=x+4 We have to find f(x) = ?…

Q: 1. Use the function f(x) = 4x°e* to answer the following problems: (a) On which interval(s) is the…

A: The given function is: fx=4x3 ex (a) To find the interval in which the function f(x) increasing?

Q: Find f′​(x) and find the equation of the line tangent to the graph of f at the indicated value of…

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Q: Determine all critical points for the following function: f(x)=12x^2+2x^3

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Q: 1. Fit the function g(x) = v1x + v2 (x – 1)3 to the data in table below. Xi -1 1 Yi 2 1 -1

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Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: Suppose thatƒ (1) = 2, that f ' (x) is the function shown in the graph below, and that k (x) = f…

A: Equation of tangent line : y - y0  = m ( x - x0 )  m is the slope of function . And ( x0 , y0 ) is…

Q: The derivative of g(x) = (1/2)* is: positive for all x O negative for all x negative for x >0 and…

A: Given function is gx=12x  ....1

Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

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Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: Q1: Find the value of the constant K if the function 4-x ;x#2 f (x) ={3-Vx² +5 is continuous at x=2.…

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Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

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Q: Q3. Discuss: max f(x), where f(x) = cos.x . (Start with a graph of the function, and confirm your…

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Q: Q 5. Find all relative extrema of the following function. f(x)=2x³ – 2x² -2x+1

A: We have to find the all relative extrema of the function: fx=2x3-2x2-2x+1 To find extrema of…

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 1. Jake the derivativeR of the function f(x)= bxtax(10+d) and list f(x) values for x= 0: 0.1:1 range…

A: # we are entitled to solve one question at a time, please resubmit the other if you wish to get it…

Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: Where is the function undefined and where is it equal to 0. f(x)=3e^2x-3

A: We can solve above question both through algebra and also through drawing it's graph. Both of them…

Q: 1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: What is the mid-line of the following function? f (x) = COS (3x − 1) + 4 3 1/3 4 -1

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Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

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Q: 2. Determine the given function is continuous or discontinuous at t=-2 (t² + 2 t -2 If f(t) = {6 t…

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Q: 5. Find the length of the curve given by the graph of the function f(x) = x/x, for a in [1,4].…

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Q: 2. The domain of the function y = 2159 / (k+1 - x^2)^(0.5) where k e R and k > -1, is:

A: The given function is: y=2159k+1-x20.5 ;       where k∈R   and  k&gt;-1

Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…