Suppose that the functions g and h are defined as follows. g (x) =x+4 h (x) = (x+5)(x-5) %3D (a) Find (-2). (b) Find all values that are NOT in the domain of . h If there is more than one value, separate them with commas.

Q: Let h(x) = f(x) – g(x). If f(x) = 5x² and g(x) = 2x³, what is h' (1)?

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Q: d the local max and min values of the function f(x)= 3x3 – 2x if it exists.

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Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Let f(x)= Vx+3 and g (x) =- x+3 Determine 3.

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Q: For what value of the constant c is the function f continuous on (-∞, ∞)? ( cx2 + 2x x3 - cx if x <…

A: We know that for any value of c, for x &lt; 5, the function is continuous and for x &gt;= 5, the…

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x < 0…

A: Here we find the value of constant a

Q: (b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x 2 Find the value of ß so that f(x) is continuous…

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Q: 1. Consider the function f(x) = -x² + 6x and the point P(2,8) on the graph of f.

A: Given data: The expression for the given function is f(x)= -x2+6x. The given point is A(2,8). (a)…

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

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Q: Let h(x) = f (X)g(x). If f (x) = In(3x² - - 4) and g(x) = 3x – 1, what is h' (x)? Select the correct…

A: Here, the given function is: h(x)=f(x)g(x)

Q: Find the linearization at x = a. f(x) = 7x³, a = 1 (Use symbolic notation and fractions where…

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Q: . If f(x) = 3x find the image and preimage of 6.

A: Given: fx=3x To determine: Image &amp; Preimage od 6.

Q: Express h(x) as a composition of two functions: h(x) = 3√(x2 + 1)

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Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: Let h(x) = f(x)g(x). If f(x) = -x - 4 and g(x) = In(2x2 – 2x – 4), what is h'(x)? %3D Select the…

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Q: 1. a) If f(x) = x-2x + 1 and g(x) =1, find f( g(-2) %3D

A: givenfx=x3-2x+1  and gx=1x2

Q: (c) Show that f(x)>0 for all values of x, x # -2.

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Q: Given f(x) = 3x – 4 and g(x) = -x² + x – 1 evaluate (f - g)(-3) %3D

A: Given that:fx=3x-4gx=-x2+x-1To find:f-g-3

Q: onsider the function: h(x) = 5 for x ≤ -4  2x+ 6 for -4<x<2 5- x2 for x ≥ 2 (D) h(−1) (E) h(0)…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: The range of the function f (x) = 2+ V9 – x² is [2, 5] O [0,3] О -3, 3] O [-1,2] O [-3,0]

A: Explanation of the answer is as follows

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−3x+4,g(x)=−x+4, and h(x)=−3x2−4x+3, what is k′(x)?

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Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

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Q: -3x² + 5x – 12, x 2

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Q: Let f(x) = 3x -2 and let g(x) = 5x + 5. Find f(x) - g(x). %3D %3D Type the coefficients in the…

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Q: Let h(x)=f(x)+g(x). If f(x)=x4 and g(x)=6x3, what is h′(−3)?

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Q: Find functions h and g such that (h o g)(x) = (x³3 + 2x – 1). -

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Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7. %3D

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Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

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

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Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

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Q: 14. If f(x)= x+4 and h(x)= 4x-1, find function g(x) such that gof =h. %3D

A: Given that , fx=x+4 and nx=4x-1We have to find gx such that got=h

Q: ) Given the function f(x) = {6 − x        if − 1 ≤ x ≤ 2…

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Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: Show that the function f(x)=x3−3x2+6x−1 is strictly increasing on R.

A: Let us find f'(x) using the power rule

Q: Let f (x) = 2x – 3x + 2 and g (a) = 6x 5x +2. What is the rule for (g- f) (x)? o (g – f) (x) = 4e² –…

A: 3rd Option  is true

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x2, what is h′(−1)?

A: Add the given two functions and differentiate with respect to x

Q: What are the critical points for the function f(x) = x³ + 9x² + 15x – 8 %3D None x = -1 and x = -5 x…

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Q: If f(x) = |x| + |x – 1| and g(x) is the piecewise function defined by: 2r-1 x> 1 0<x<1 1- 2r x<0…

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Q: 7. Find the domain of the functions. a. g(x) = 4 +x – V3 – 5x. 7x3-x²+16 b. f(x) х2-21х-100 In(7-3x)…

A: 7 a Given function is : gx=4+x-3-5x For function gx to be defined if , 3-5x≥0-5x≥-3x≤35   Thus , the…

Q: If f(x) = 5x - 2, g (x) = – 2r + 3 and h (x)= x, then (fogoh)(-2)=.... %3D

A: The functions are f(x)=5x-2g(x)=-2x+3h(x)=x3 If f(x) and g(x) are two functions then the composition…

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

A: The function fg is defined by fg(x)=f(x)g(x)

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

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Q: Let h(x)=f(x)−g(x). If f(x)=5x2 and g(x)=2x3, what is h′(1)?

A: Consider the given functions, fx=5x2 and gx=2x3 Since it is given that hx=fx-gx so substitute the…

Q: Find the value for k so that the function will be continuous at x = 2. 4x2 – 12x + 8 6 if x 2

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Q: The domain of function x) = In(2– x) is %3D

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Q: Find  a and b  such that the function f(x)={x^2+4x+8 if x_&lt;1         {ax+b if x&gt;1

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

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Q: Let g(x)= x-2/x+5 and h (x)= x+1/x+5. Then (h+g) (x) is equal to?

A: Topic  =Function

Q: Given f(x) = 2x - 3 and g(x) =x -1, compute g(f(5)) (x)f uaa

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Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4