uppose that the functions g and h are defined as follows. g (x) = -5+3x? h (x) = 4-9x a) Find |(-4). h

Q: Let h(æ) = f(x)+ g(x). If f(x) = 7x³ and g(æ) = 9x4, what is h' (æ)? Do not include "h' (7) =" in…

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Q: Consider the function f(x)=x^3-3x^2-9x+7 Find the values of x such that f'(x)=0

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Q: (c) Determine the values of x for which the function f (x) = {x+ 2 2x2 x5 is discontinuous. x25

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Q: ALUATE THE FUNCTION, if g(x² - 3); evaluate g(x) = 3-x/3+x

A: We have g(x)=3-x3+x to evaluate gx2-3

Q: 6x Given f(x) = is one-to-one, find f-(x). x+2

A: Given that        f(x) = 6x/(x+2)  Here we have to find f-1(x).

Q: Find the domain of the following function. Express the domain in interval notation. g(x) = V4 – x -…

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Q: f (h+4)-f (4) (***) Use the function f (x)=3x² – 5x to evaluate

A: Given,

Q: 2. Write TRUE if the statement is correct. Otherwise, FALSE. 5x, x-1/2 Let g(x) = .At x = -1/2, the…

A: True or False  Consider the function: gx=5x       ,  x≤-1212x+1,  x>-12. Check continuity and…

Q: a) Find the intervals at which the function is increasing or decreasing. x2 f(x) = 16 – x2

A: f(x) = x²/(16 - x²) So, f'(x) = [(16 - x²)•2x - x²•(-2x)]/(16 - x²)²  So, f'(x) = 32x/(16 - x²)²…

Q: 1. Find the domain of the following function and express it using interval notation: X +1 h(x)= -x-6

A: Solution: The objective is to find the domain of the given function

Q: The function h is defined by h (x) = 2x+4. Find h (x-3). h (x - 3) = [|

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Q: 9. What is the domain of the function f(x) = Vx- 3? | A. (3, 0) B. (-00, 3] С. [3, о) D. (-00, 3)

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Q: Sx² + 2 , lx² – xk – 3 , x 5 10. Find the value of K that makes the function f(x) = Continuous at x…

A: We have to find k

Q: (4x + 7 (ii) If f(x)={ 4x -1 18xs2 , determine whether the function f(x) is continuous 2<x<4…

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Q: 5. If f(2) = 5 and f (-1) = -4, find a and b in the function f(x) = ax + b

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Q: A) Define the term function. B) Find fo g (x) if f(x) = 4x-11 23x+17 and g(x)= 3x²-7 5x²+2

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Q: Consider f(x) =x² – 3x. In which interval is the function decreasing? [-1,0] [3,4] [0,1] [2,3] [-1,…

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Q: snip

A: Find the domain of the function.         fx=x-1x+4

Q: Q4: Evaluate the function at the given values f(x) = v20 – x² when x = - 4

A:

Q: The function f (x) = 2x² + 6x – 12 has a domain of all the whole numbers in which -2 sxs 1. List the…

A: Given,          The function fx=2x2+6x-12 has a domain of all whole numbers in which -2≤x≤1.

Q: 5. Find all points of inflection of the function g(x) = x²e¬x.

A: using double derivative

Q: 2. Rewrite the function f(x) =-3(x+2)-3 in the form f(x) =ax+bx+c.

A: The given function is, f(x)=-3(x+2)2-3. Rewrite the given function as follows.…

Q: Let h(x)=f(x)+g(x). If f(x)=2x2 and g(x)=8x5, what is h′(x)? Do not include "h′(x)=" in your answer.…

A: We have been given h(x) = f(x)+g(x) and f(x) = 2x^2 and g(x) = 8x^5So we can first write a function…

Q: Find ƒ″(x )  for function. Then find ƒ″( 0)  and ƒ″ (2) . ƒ(x) = -6x1/3

A: Find ƒ″(x )  for function. Then find ƒ″( 0)  and ƒ″ (2) . ƒ(x) = -6x1/3

Q: The discontinuities of the function f(x) =D 4x-9 are: x²-2x-15 Select one: O 5,3 -5, -3 -5,3 O 5,-3

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Q: Determine the values of x for which f (x)=x",x >0 is increasing or decreasing.

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Q: 5. Given f(x) =-x+ 3 and g(x) = 2x2 – 5, find the value of f (0) + g(1).

A:

Q: Let h(x) = f(x) + g(x). If f(x) = 2x² and g(x) = 8x5, what is h'(x)? Do not include "h' (x) =" in…

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Q: x - 7 If f(x) = Vx – 3 and g(x) find the domain x - 4 of

A: Given: f(x)=x-3 and g(x)=x-7x-4 To find: Domain of fgx.

Q: 2x4 -Vx+x 7xcsc² x+1 Find all functions g such that g'(x)=4sinx+

A: g'x=4sinx+2x4-x+xx-7xcsc2x+1x

Q: Find the domain of the function.

A: Domain : All possible value of x in f(x)f(x) = 4x +4+8x-14

Q: find the function h such that h"(x)=36t2 +24t-4, h'(1) and h(-1)=1

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Q: Use the function f(x) =3x2-5x,g(x)=6x-4,h(x)=5-x3 find the (gof)(x)

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Q: See attached

A: The given function:

Q: Use the function f (x)=3x²- 5x, g (x )=6x-4, h(x)=5 - x' ind the (gof)(x)

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Q: Find the domain of the function. f(x) = x2 – 10x – 14 What is the domain of f? O A. (-00,00) O B.…

A: Answer is- Option A is correct

Q: Q2-find the domain and range of these functions A) f(x)=4-x2 B) f(x)={-x D) f(x) = x

A: (A).  The given function is: f(x)=4-x2 Here  x∈(-∞, ∞). Hence the domain of the given function is:…

Q: x² + 5x + 7 On what domain is the function f(x) continuous? x + 7

A:

Q: Let f(x)=16x+1,  −4≤x≤1 The domain of f−1f-1 is the interval [A,B] where A=?? where b=???

A: fx=16x+1,  -4≤x≤1 When x=-4, f-4=16-4+1=-63 when x=1, f1=161+1=17 Therefore the range of fx is -63,…

Q: Find f such that f'(x)= 1(4)= 20.

A:

Q: f(x) = What is f(-1 -2

A: When x =-1, f(x) = 2x+3

Q: Express the function,h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given, hx=2x-53

Q: Using f(x)= 3x-2x+2, find and simplify the difference quotient S(x+h)- f(x) 2)

A: The difference quotient: The differentia quotient of a function fx is: f(x+h)-f(x)h The given…

Q: 3x Consider the function f(x) = x2 +4x-5 For what value(s) of x is the function undefined?

A: The given function,   fx=3xx2+4x-5

Q: 5x Determine the values of x for which the function f (x) = is discontinuous. x2+x

A:

Q: Find f+g, f-g, fg and f/g and their domains.  f(x)=2/x , g(x)=4/x+4  Answer should be:

A: we have given f and g  We have to find the value of f+g, f-g, fg,f/g and their domain

Q: 8. A student writes the following for the function f(x) 2 x¯- 8x+8 “ The domain of f(x) is (-∞, -4)…

A: Consider the given function as fx=x-2x2-8x+8

Q: Find the value for the function. 3) Find f(4) when f(x) = Vx2 +.

A: The given function is, fx=x2+3x. The objective is find the value of the function at x=4.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: