Evaluate the piecewise function at the given value of the independent variable. f(x) = [x - 1 ={x - if x>-3. 1-(x - 1) ifxs-3 f(-5) A) 6 B) -6 17

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: Evaluate each expression using the functions

A: Given; f(x)=xx-2 Let  f∘gx=x⇒f-1=g We have, f(x)=xx-2 Assume,…

Q: Express the function,h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) = (f ∘…

A: We will take the inner function as g(x) and the outer function as f(x). Note that 2x-3 is inside.…

Q: Which of the following is the appropriate function used in finding the value of. V2-1 f(x) =x² -…

A: f(x) =x^2 - 2x-1

Q: Find f(x) if F is a linear function such that f(6) = -7 and f(-2)=2  f(x)=

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Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: f(x) = xe-x²/128 [-2, 16]

A: Let's find.

Q: Let f(x)=x^3-3x^2-3x+9. For what values of x is f'(x)=0? What are the local max and min points for…

A: Given  f(x) = x3-3x2-3x+9 ∴ f'(x) = 3x2-6x-3

Q: 6. Determine all values of x at which the function is discontinuous. x2- 2x +5 f(x) = x2-4x 0, 4 O…

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Q: Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = 1x. Find the functions. f (x) + g(x)

A: Since, we have been given that:-f(x)=x2-2x -(i)g(x)=3x-1 -(ii)and h(x)=x -(iii)Our Aim is to find…

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

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Q: 4. Given the function f(x) = x3 In x. Determine the following: a. Domain b. X intercept(s)

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Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is - concave upward on O (-∞0, 2) O (-∞, ∞0) O (2,…

A: The given function is: f(x)=x3-6x2+9x+1

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: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

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

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe-x²/98…

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Q: Find ao of the function f(x) =(n - x)? – x)² |3D |

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Q: Evaluate f(-2), f(-1), and f(3) for the piecewise defined function. Sx + 3 f(x) = {? if x -1 f(-2)…

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Q: A function f is ________ on an interval when, for any x1 and x2 in the interval, x1 < x2 implies…

A: To fill: The blank of the statement. Given: The statement is "A function f is ________ on an…

Q: Consider the function: f(x) = 5x* – 2x³ + 3 Show that there is a value a e [0,2] such that f (a) =…

A: This question is based on continuity of function.

Q: Express the function h(x) = (3x - 1)4 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given: h(x) = (3x - 1)4

Q: 7. If f(x)=4x-3 and h(x) = 4x² -21, find a function g such that fog=h

A: The given functions are: fx=4x-3 and hx=4x2-21

Q: Let f(x)=(x-3)/(x2-1).  What can you say about the long-term behavior of f?

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Q: Find the function f °g and its domain if f(x)= x-1 and g(x) = x+5

A: Domain of the function is the set of all its possible inputs for which function is defined

Q: Find the value of a that makes the following function differentiable for all values of x. ax if x<0…

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Q: Please show step-by-step solution

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Q: A linear function is described either verbally, numerically, or graphically. Express f in the form…

A: Solution: Consider the given figure and we have to find the equation of the line; Let f(x) = ax + b…

Q: Find a number c such that the function f(x) = 6 -2x can be written in the form f(x) = c".

A: Givenf(x)=6-2x

Q: b. Suppose the function h is defined as h(x) = 3f(x). Determine the domain and range of h.

A: b. Given that  h(x)=3f(x) Domain of f is [0,4] and range [0,2]

Q: 39. Let f(x) = 2x3 - 4. Find a function y = g(x) so that (f o g)(x) =x+2.

A: We use the definition of composition of functions to find y= g(x).

Q: Let h(x) = f(x)g(x). If f(x) = x² + 4x – 1, 9(-2) = 3, and g'(-2) = -5, what is h' (-2)?

A: Given h(x) = f(x)g(x). ƒ(x) = x² + 4x − 1, g(−2) = 3, and g'(-2) = −5,

Q: Find functions f and g such that h(x) = f(g(x)), when h(x) = (9x³ – 5x)³ – (9x³ – 5x)² + 11.

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Q: let f(x)=-2x^2-x, and let g(x)=f(x)-f(-1)/x+1, x not equal to -1. find g(10).

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Q: Find f •g and gof ,where f (x) = x² + 1 and g(x) = x + 2, are functions from R to R.

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Q: Express the given function h(x) = 3√(x2 - 9) as a composition of two functions f and g so that h(x)…

A: Given function is  h(x)= x2-93.

Q: Find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

A: Consider the given: Fx=∫1x20v2dv Find the…

Q: the domain of the function : y = In(x² + x + 1) is [0,0) Select one: O True O False

A: From the given problem:   y=lnx2+x+1   We know that logax is defined when x,a&gt;0.

Q: Find the domain of the function. f(x) = -2x - 9 O (*, *) O (0. *) (-* 0)U (0, *) 19 *)

A: Given that f(x)=-2x-9 To find the domain of f(x).

Q: Let h(x)=f(x)g(x). If f(x)=x^2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)?

A: We have to find function

Q: Express the function h(x)=1x+8h(x)=1x+8 in the form f∘gf∘g. If g(x)=(x+8)g(x)=(x+8), find the…

A: The given function is h(x) = x + 8.We have to express it as a composition of two functions f(x) and…

Q: Express f(x) in the form f(x) = (x- k)q(x) + r for the given value of k. f(x) = 2x3 + x2 + x- 5, k=…

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Q: Find F as a function of x and evaluate it at x = 2, x = 4, and x = 6. F) - [- Part 1 of 8

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Q: 4. Given the functions f(x) = x + 2 and g(x) = x², determine all values of x for which f(g(x)) =…

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Q: 1 The functionf is defined by f(x)= 2–Vx+ 5 for-5<x< 0. (i) Write down the range of f.

A: The objective of the question is find the range of the function f(x). And  solve the composition of…

Q: f f(x) = x? + kx + 1 for all x and f is an even function, f

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Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is concave downward on O (-∞, 2) O (-∞, ∞) O (2, c0)…

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