The function f and g are defined as follows. A. -3 or f(x)%= In(x+1), x>-1 8(x)=x² +2x , x>-1 B. -3 -1 or C. 3 -1 or Find the values of x if (og)(x)3e-1. D. 3 or

Q: 4. f (x) = 5 - x and (gof) (x) = x2-10x + 30 since the function g(x) is the following- which is…

A: The solution is:

Q: G' (x) = 2xex + x 2ex, and this is not equal to f (x). However, H'(x) = 2ex + 2xex - 2ex = 2xex = f…

A: Given Data The derivative function is G’(x)=2xeˣ+x2eˣ. The another derivative function is H’(x)=…

Q: The domain of the constant function g (x) = k is ________, and its range is _______ .

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Q: A square root function is given below. h(x) = --3 - Which function opens in the same direction and…

A: Given : h(x) = -12x - 3 - 2   To find the function.

Q: Given that g(2)=4 and g'(2)=3, what is the value of h'(2) for the function h(x) = In(g(x))? O 4/3 O…

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Q: (;) 9 and () ). For the functions f (x) = 4x4 – 19x³ – 10x2 + 35x – 50 and g(x) = x – 5, find E) (x)…

A: Consider the provided functions, fx=4x4-19x3-10x2+35x-50    and    gx=x-5 Find the value of fgx…

Q: (r-1) (x-1) If f(x) = (2x+5) and g(x) = then the function (2) (x) is (2x-5) (2x+5) a) (E) (x) =…

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Q: Based on the graphs of f(x) and g(x), in which interval(s) are both functions increasing?…

A: Domain of g(x) can be broken into following intervals: (-inf,-3), (-3,-1) and (-1,inf) In each…

Q: A study indicates that spending money on pollution control is effective up to a point but eventually…

A:

Q: Find f' (2) and determine the value of x for which f'(x) = 0 a) f'(x) = ln2x - 2x b) f'(x) = (2x…

A: Two functions are given by, f'x=ln2x-2x and f'x=2x-85. The objective is to find the value of f'2 and…

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

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Q: The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)is…

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Q: If p(x) is the total value of the production when there are x workers in a plant, then the average…

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Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: For which of the following decreasing functions f does (F')'(10) = - ? 8. A f(x) = –5x + 15 В f(x) =…

A: Consider the provided question, Given, f-1'10=-18 We know that,f-1'fx=1f'x    ......(I)Compare (I)…

Q: f(x)=−4x+4​,g(x)=−5x2+5x−4​,andh(x)=−3x2+8​, find h(−1​).

A:

Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x² - x + 13 b)…

A:

Q: The population of a city is expected to be P(x) = x(x2 + 16)−1/2  million people after x years. Find…

A: The population of city after x years is  Px=xx2+16 We have to find average population between year…

Q: the

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Q: 7. The graph of f (x) and a table of values for g(x) and a'(x) is given. If h(x) = /f(x)· g(x) %D…

A: (3) Given that fx=-xx-1. To determine whether fx is increasing, decreasing or has a horizontal…

Q: let f(X)=5x +(-3) find the largest & sothat [fx)-F(a]]<E when(x-a/<8

A:

Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: If f(x) = -1) (2x+5) (x-3) then the function (E) (x) is (2x+5) (x-1) and g(x) = a) ) *) = 1 (x-3) b)…

A: We have to find fgx where functions are given as: fx=x-12x+5 and gx=x-32x+5. We know from operation…

Q: B. Evaluate the piecewise function below at the given values of x. if -1 1 1.f(-1) 2. f(5) 3. (e)

A:

Q: 1. Given f(x) = -2x and g(x) = x - 7, find g(f(2)). *

A: f(x)=-2x g(x)=x-7

Q: Consider the following. P = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

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Q: Given the function f(x)=In(ax+b), which of the following is true so the function is increasing at .?…

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Q: 14. Find the intervals over which the function is increasing or decreasing. y = 5x 2 + 6x - 4

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Q: Xi -3 -1 0. -2 1 f(xi) 7.1 -4.3 -3 -2.6 -0.6 Given that the above data was extracted from the…

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Q: Q1/ Find the maxima, minima and saddle points for the following function and the value of the…

A: Since you have asked for multiple questions, we will solve the first question for you. If you want…

Q: Find the zero of the linear function: (d)  f(x)=5x−25 (e)  f(x)=−x+7 (f)  f(x)=23−x (g)…

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Q: 30) Which function has a range of y > 4? A) f(x) = (x-2)² + 4 B) f(x) = |x-2| - 4 C) f(x) = 3x+4 D)…

A: The solution of problem 30 is given in the next step.

Q: The population of a city is expected to be P(x) = x(x2 + 64)−1/2 million people after x years. Find…

A: We will use the average of a function formula

Q: Q3) A) If you have three functions: f (x) = x² – x g(x) = 3x – 1 w(x) = x² – 2 So, find gof (x) and…

A:

Q: Find those values of x for which the given function is increasing and those values of x for which it…

A: For function to be increasing or decreasing consider f'(x)

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

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Q: Given the function f(x)=ax =axın( x+b), which of the following is true so the function is decreasing…

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Q: Consider the following function.   g(x) = 2x2 + (32/x)+8   Find the x-value(s) of the relative…

A: We find the first and second derivative using power rule. Power rule: d/dx(x^n)=n*x^(n-1)

Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x²-x+ 13. b)…

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Q: Find the largest interval on which the given function is increasing. a. ƒ(x) = 0 x - 2 0 + 1 b. ƒ(x)…

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Q: 15. The range of values ofx for which the function f:x+x² – 6x + 4 is increasing is A x>3 B x 3

A: To find the range of x for which the given function f(x) is increasing

Q: Find functions f and g so that h(x) = (f g)(x). 8 3) h(x)= N8x+2 A) f(x) =8/x, g(x) = 8x+2 C) f(x)…

A: We have to find f and g so that  hx=fogx Now, hx=88x+2 we know that composite function fogx=fgx…

Q: If f and g are functions of time, and at time t = 3, fequals 7 and is rising at a rate of 5 units…

A: f(3)=7df(t)dt=5g(3)=6dg(t)dt=7

Q: A function has f''(x) = 10 and has f'(4) = 0 and f(2) = 4. Find f(x).

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Q: Q3\ a) Find the values of a and b to make the functions continuous at every x: ax + 2b 2) g(x) = }x²…

A: Given function is,  f(x)=-2        ;x≤-1ax-b   ;-1≤x≤13          ;x&gt;1

Q: For what value of "a" and "b" given function is coutinuous a + 2b , x > 2 -1 < x < 2 x<-1 g(x) х2 +а…

A: We have to use application of continuity.

Q: Is the function of k(x)= 9^x/7*7^x exponential? If so, write the function in form k(x)=ab^x

A: Consider  the function

Q: 4- Legendre function of P4(x) equal to : a) P,(x) = (35x* – 30x? + 3) b) P, (x) =(35x* – 30x? + 3)…

A: Given:        The Legendre Equation is given as                1-x2d2ydx2-2xdydx+nn+1y=0 The…

Q: Find the domain of the function.(a) f(t)= ln(2t-3)

A: The given function is: f(t)= ln(2t-3) Since logrthmic function is not defined for non-postive…

Q: 2. Each of the following tables shows a collection of points (x, f (x)) from a function f. For each…

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