1 The function h(x) : can be expressed in the form f(g(x)), where g(x) = (x – 9), and f(x) is %3D x – 9 defined as:

Q: (f + g - h) (x) f(x) = x + 4 g(x) = 2x2 + 2x h(x) = x² + 1 %3D O x2 + 3x + 5 3x2 + 3x + 5 O x2 + 3x…

A: We use the sum and difference of functions to answer the given question.

Q: S2x³ – 18x + 11 x² – 4x + 3 ln(x) x 21 x < 1 (you may assume g is continuous). Find all critical…

A: Given   function gx=2x3-18x+11        x&lt;1x2-4x+3lnx         x≥1

Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.…

A: Given: fx=4-x2, fx=x2-16, fx=x-12 We know that any given functionfx is increasing in a interval if…

Q: f(x) = x³ e* on [-1 , 5]

A: Let the function be f(x)=x3e-x. Differentiate the function with respect to x implies,…

Q: f(x) = 3x + 5 g(x) = 4x² – 2 %3D h(x) = x² – 3x + 1 Find f(x) - g(x) – h(x). O - 5x + 6x + 6 O -5x +…

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Q: „2 - 5 Differentiate: f (x) = ln x4 f'(x) =

A:

Q: 3. GIVEN: ƒ(x): 2x2 – 3 xs2 (8x-11, x>2 DISCUSS THE DIFFERENTIABILITY OF THE GIVEN FUNCTION AT x = 2…

A: Given query is to determine whether f(x) is differentiable at x=2 or not.

Q: 1. If the graph of y = f(x) contains the point (0,2), and f(x) > 0 for all x, then f(x) = dx (a)…

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Q: 1. Differentiate the following and for each state whether you have used the product rule and/or the…

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Q: f(x) = e + x³ – 1 and g(x) = 2r2 – 1. %3D Find (g of-)(e). · O C

A: Please refer to the image below

Q: The function f(x) = (4x + 8)e has one critical number. Find it. 4x %3D X =

A: Recall:   1.) For critical numbers , f'(x) =0 .2.) Product Rule of differentiation :…

Q: 12. Find the domain of f (x) = ln x- 5 x+7

A: given,

Q: 3 (d) h (x) = 3x² – 4x2 + 2 | (e) ƒ (x) = x5 – xª + x³ – x² + x – 1 - | (f) ƒ (x) = x6+x5+x4 – a³ –…

A: Here we have to find  The derivative of the given functions d)…

Q: A-l1* Px = \* F« = X*(\E – 1)-' Px 1 = A*. X(1+A) – 1° -Pk 1 (1 A - 11+ XA/(A – 1) 1 1 X- 1 (A – 1)²…

A: We have to explain Binomial expansion :

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

A: (1) Given functions are  f(x) = (2x2-1)(x2+3)x2+1  and g(x) = (x2+8)7(2-3x2)5

Q: 2. If f(x) = x-1 and g(x) = - x2+ 2 a) Find (fog)(x)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: x-1' Find the value of the constant A for which the follo

A: Find the value of A

Q: The population of a city is expected to be P(x) = x(x2 + 36)−1/2  million people after x years. Find…

A: Given function is The average value of population between year x = 0 and year x = 8 is

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

A:

Q: 16) g(x) = 4x - 5 s(x) = x' + x² Find (g + f)(-2)

A: Given,      g(x)=4x-5      f(x)=x3+x2

Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: The Gini index, given by 2∫10(x−f(x))dx2∫01(x−f(x))dx, is a measure of a country's income equality…

A: 2∫01(x-f(x))dx    , f(x) = x5.3

Q: F(x)=e^2x (3x^2-x)

A: see 2nd step

Q: Find f’(e) of the following function. f(x)= x3 *(ln x- 1/3)

A:

Q: 9. f(x) = 2x + 2, h(x) = -2x – 5 find (g o h)(-4 + x) 10. f(x) = 2x, g(x) = -x – 4, find (f o g)(x)

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Q: 5/A) Find for the function dx V2x - 3 (x+ 2 y =- V3x - 2 Find the Domain of the following function x…

A: We have  y=2x-3x+223x-23 differentiate with respect to x dydx=ddx2x-3x+223x-23

Q: 1) Using g(x) = x + 3, f(x) = x² and find (f o g)(x)

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Q: 9. E Find the absolute maximum and the absolute minimum values of the function f(x) = x- 27x + 11 on…

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Q: Iff(x) = 1 %3D Зх-1 and g(x) = f-' (x), find g' (x). 1 o g'(x) = -, 3x2 o g(x) %3D뉴 1 2r2 1 o g'(x)…

A: Given f(x)=y=13x-1f-1(x):Replace x with y and solve for yx=13y-13y-1=1x3y=1x+1y=x+13x

Q: (2x² - 2x 4 B) For what values of k and h is y={ k + 2x 2 + hx2 - 2 < x<-1 - 1<x< 2 2 <x<4…

A: B) Given, y=2x2-2x-4, -2≤x&lt;-1k+2x, -1≤x≤22+hx2, 2&lt;x≤4 and also continuous at x=-1, 2.  We have…

Q: 1 Let f(x) = 5x° - 9x - 3, x2 1.5. Find the value of - df at the point x= 1271 = f(7). dx

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Q: 25. lim h→0 (x+h)² +4(x+h) —x²− 4 at h (A) x³ + x4 (B) x² + 4x (C) 2x+4 (D) nonexistent

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

A:

Q: f(x) = x – 1 m(x) = 3x + 2 h(x) = -4 g(x) = x2 – 5x + 4 4. (m • g)(x) 5. (mof)(x) 6. (g - f)(x)

A: (m×g)(x)=m(x)×g(x)given:m(x)=3x+2 and g(x)=x2-5x+4(m×g)(x)=(3x+2)(x2-5x+4)=3x3-13x2+2x+8

Q: Sf(x) – g(x) if f(x) ² g(x) lg(x) – f(x) if g(x) ² f(x) \f(x) – g(x)| %3D we obtain the formula…

A: Given: 1. f,g and h are continuous on [a,b]. 2. 3. To show: The area (A) of the region between the…

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: (a) Express the new function m(x) = ln in terms of the original function g(x) In(x). m(x) :

A: Given- mx=lnx2and gx=lnx To find- The value of mx in terms of gx. Formula used- lnab=lna-lnb

Q: f(x) -ax e = X <0

A:

Q: 02. Find the end behavior for y = x–9x+20. A. x + +0, f(x) → +∞ ; x → -o, f(x) → +∞ B. x → +0,…

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Q: x% (x-4)* Find the critical numbers of the function g(x) =x 2.

A: Compute the derivative of the above function.

Q: 5. A function, f(x), has two zeroes at (-9, 0) and (7, 0). The leading coefficient of f(x) is a= -…

A: Given that a function “f (x)” has two zeros at (-9, 0) and (7, 0) and the leading coefficient of the…

Q: [3 Marks] B1(a): Determine whether the function e12x x 0 %3D 12x 1 - [3 Marks] B1(b): Solve the…

A: Follow the steps .

Q: g(x) = (9) Find the critical values for x² + 4x+4 X

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Q: lim f(x+h)-f(x) h-0 3x f'(x) = ? %3D h x+1

A:

Q: (a): Find the value of k that makes function continuous at x = 4 %3D S 2x + 8 x > 4 x < 4 f(x) = 5x…

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

Q: :h(x) = f(g(x)) %3D 1) h(x) = x2-5 2) h(x) : +3 x2-7 3) h(x) = (x2 + 5x – 1)700

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: 4. f(x) = 10-5x² 5. f(x) = e[ 6. f(x) = /In(e 3x + a³x) %3D

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Q: What is the domain and range of g G(x)= 3 ln(x) +2

A: