Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by, H(x) = x - |x – 2|.

Q: Find the domain of the function. G(x) = √(1 - x)

A: To find the domain of the function

Q: compute f(x)-f(a)/x-a for the following function f(x)=x^2-3x+1

A:

Q: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

Q: Let f(x) = x³ + 2, g(x) = x- - 3, and h(x) = 8x + 3. Find the rule for the function. %3D f-g

A: Given function is : fx=x3+2gx=x2-3hx=8x+3  To find the value of fx-gxhx

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

A: h(x) = |3x - 4| To write h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x)…

Q: Consider the functions f(x) = x +7 and g(x) = 27 - x2. (a) Use algebra to find the x-values where…

A: f(x) = x+7g(x) = 27 -x2calculating intersect points :f(x) = g(x)

Q: Express h(x) = (x2 - 3x + 7)9 as a composition of two functions f and g such that h(x) = ( f ∘…

A: To Determine:  Express h(x)  as a composition of two functions f and g such that h(x) = ( f ∘ g)(x).…

Q: f(x) = xe-x²/128 [-2, 16]

A: Let's find.

Q: Use the graph of the given function f(x) to find x such that f(x) = - 3. 2- ->

A: f(x) implies y in a cartesian plane so the value of y is the value of f(x)

Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: Find the domain and sketch the graph of the function.

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Q: If ƒ and g are real-valued functions, how are the domains of ƒ + g, ƒ - g, ƒg, and ƒ&gt;g related to…

A: Take f:D1→ℝ and g:D2→ℝ. Then, the operation f+g is only possible when the domain is D1∩D2. That is…

Q: Apply the intermediate value theorem  evaluate the function f(x)=x^4+8x+3 at each endpoint of the…

A: Given,         The function is fx=x4+8x+3 at each endpoint of the interval -1,0.

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

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Q: Find the value of k that will make the function f(x) continuous. -x2+8, if x+ 3 f (x) =, k, if x=3

A: topic - limits and continuity

Q: For the function f defined by f(x) = x2 - 4x + 1,

A: Given function: fx=x2-4x+1

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

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Q: Consider the function f(t) = = -X 3-x (x − 3)² - if x 3

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Q: Express h(x) as a composition of two functions:    h(x) = ∛( x2 + 1).

A: Given: h(x)=x2+13 To find: The composition of two function. That is h(x)=f(x)∘g(x)

Q: Determine whether the function of f(x) is continuous at x = -1 x2 -1 f(x) ={ x +1 X + -1 -2 X = -1

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Q: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

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Q: Find the most general function F such that F'(x) – 14. x5 || - F(x) = Σ

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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: Let f(x) = x - 5 and g(x) = x2 - 1. Find the function: (f - g)(x)

A: Given, f(x) = x - 5 g(x) = x2 - 1

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 the domain and sketch the graph of the function.

A: fx=x+2    if x≤-1x2        if x&gt;-1 The domain of given function is the set of all real numbers.

Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², (2x + k,…

A: Answer: The solution is as given below:

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: Differentiate the function.

A: The given function is ,gx=lna-xa+x the above function can be written as, gx=lna-x-lna+x…

Q: What is the end behavior of the given function? f (x) = 3V-x – 2 As x → 0, f(x) → -∞. As x → -, f(x)…

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

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Q: Let f(x) = x3 + 3, g(x) = x2 - 3, and h(x) = 3x + 3. Find the rule for the function. fgh

A: Use the rule of composite functions.

Q: Find all values of x such that f (x) &gt; 0 and all x such that f (x) &lt; 0, and sketch the graph…

A: f(x)=x4-4x2=x2x2-4f(x)&gt;0⇔x2x2-4&gt;0⇔x2&gt;0 and x2-4&gt;0 or  x2&lt;0 and x2-4&lt;0⇔x∈ℝ \ 0 and…

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: Find the domain of the function. g(x) = In(x - x2)

A: The domain is the set of values for which the function is defined or gives a real number as an…

Q: Let ( 3x² + 2, f(x) = { 2x - 3, be a piecewise function. Evaluate 5 Sof(x)dx= 3 if x < 3 if x ≥ 3

A: The given function:fx=3x2+2if x&lt;32x-3if x≥3.We need to find ∫35fxdx.

Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

A:

Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: to determine if the function is differentiable we have to check if it's differentiation is equal…

Q: Determine the value of x of the discontinuous function: * x – 1 x 3

A:

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: Given that f(x) = 5x – 13 where f(x) = y, define a function rule for f-1.

A: Given function, fx=5x-13 The objective is to find the inverse function. y=fx⇒f-1y=x The following…

Q: ) Determine the Range of the function g(x) = x³ for the Domain: {-1,0,1}

A:

Q: Let f(x) = x² + 2, g(x) = x-- 3, and h(x) = 8x + 3. Find the rule for the function. %3! %3D %3D f-g

A: Consider the given function as, fx=x3+2, gx=x2-3 and hx=8x+3

Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: Express the function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

Q: 2. Let f be the function defined by 9) f (x) = x²+2x+1 ,Find: -f (3) +fヒ3)

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Q: Evaluate the given piecewise function at the given points 2x +1, x 2 1 f(x) = %3D x2 +3, x< 1 at…

A: We need to find value of f(-2) and f(6) for piecewise function