Evaluate: f(g(0)) y = f(x) y = g(x) 10 10 9 9. 8. 8. 7. 7. 6. 5 4 3 1 1. -10-9-8-7-6 7-4 -3 -2 -1 2 3 45 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 - -2 - 23456 7 89 10 -2 -2 -3 -3 -4 -4 -5 -6 -5 -6 -7 -7 -8 -8 -6- -9 -10 -10

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

A:

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

A: The given functions are fx=4x2-3x and gx=ln3x-1. Here,  hx=4x2-3xln3x-1.

Q: Let h(x)=f(x)g(x). If f(x)=3cos(x) and g(x)=3x3 +2x2 −x+4, what is h′(x)?

A: f(x)=3 cos (x) g(x)=3x3+2x2-x+4 h(x)=f(x) g(x) We need to find h'(x)

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

A:

Q: 2 Describe the long run behavior of f(z) = As a + - 00, f(x) V ? As z + 00, f(2) + ( -00

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Q: The critical points of the function f(x) = 25x2 – 2x occur at x = 0, x = ±10.00 x = 0, x = ±1.25 x =…

A:

Q: Evaluate: f(g(6)) y = f(x) y = g(x) A10 10 9 8 8 6. 6. 5 3 3. 1 -10-9 -8 -7-6 -5 -4/-3 -2 -1, 1 2 3…

A:

Q: 1) Simplify the expression for f(x + 1) - f(x) where f(x) = e2x - 1) . ) 0 (2 - 1) b) O (2-1)(2 - 1)…

A: option (b) is correct. see below the calculation

Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

A:

Q: Evaluate: f(g(-8)) y = f(x) y = g(x) 10 9. 6. 4 4 -10-9 -8 - -6-5-4 -3-2 - 1 2 4 5 6 7 8 9 10 -10-9…

A:

Q: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

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Q: Find (f/g) (n) when f(n) = x^2 - 3x - 4 and g(n) = x + 1 _____________________ A. x + 2 B. x - 1 C.…

A:

Q: Evaluate: g(f(-8)) y = f(x) y = g(x) 10 10 4 3 -10-9-8 -7 -6 -5 -43 -2 -!, 1 2 3 4 6 7 8 9 10…

A: Firstly we find the value of f(-8).

Q: Let h(x)=f(x)g(x), where f(x)=−2x−3 and g(x)=x2−x+2. What is h′(x)?

A: we have to find the derivative of h(x)

Q: Compute (f.g)(x) for f(x) =4x-1, g(x)=√6+7x

A:

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…

A:

Q: Evaluate: f(g(0)) y = f(x) y = g(x) 10 10 9 8 7. 4 4 13 3 -10-9-8 -7 -6 -5 -4 -3 -2 -1, 3 45 6 7 8 9…

A:

Q: a) Differentiate the following with respect to x. i. S (x)=(x +3)° ii. f(x) = (3x² +7)(6- 5x ) 2…

A: We have to the basic formula for differentiating x^n for a).

Q: Question 4 options:   14x + 7h + 6   14x + 6   21x - 9h + 12   14x2 + 7h + 6x

A:

Q: x f(x) | f(x) | g(x) | g'(x) 1 1 1 3 -2 1 2 1 -- 2 3 1 1 Find h' (3) given h (x) = f (g (x)) and…

A: x f(x) f'(x) g(x) g'(x) 1 1 1 3 -2 2 2 1 1 -12 3 3 1 2 1

Q: Evaluate: f(g(-5)) y = f(x) y g(x) 10 10 8. 9. 7. 6. 4 13 2 -10-9-8 -7 -6 -5 -4 -3 --1 123 5 6 7 8 9…

A: We have to calculate f(g(-5)) using the graph of f(x) and g(x). To do so, we need to calculate g(-5)…

Q: y = f(x) y = g(x) 10 10 9. 8. 9. 7. 7. 6. 4 3 3 2 1. 1 X. -10-9 -8 -7 -6 -5 -4 -3 -2 1 2 3 45 67 8…

A:

Q: 2.Find an example different from the one in the text showing that (f ∗ 1)(t) need not be equal to…

A:

Q: Evaluate: g(f(7)) y = f(x) y = g(x) 10 10 6. 6. 8. 7. 5. 4 3 1. -10-9 -8 -7-6 23 4 678 10 -10-9…

A:

Q: he table below gives values of f(x) = e f(x) fx) 0.94 0.95 0.96 0.97 0.98 2.55998142 0.99 2.69123447…

A: Given: Here the given is f(x)=ex. We have to compute f'(1.0) and f''(1.0) with the following data…

Q: 10- -7- 67 5- 4- -4 -3 -2 -1 For the above function f( x ) = 6- 1.15", estimate f'(x) using h 0.001…

A:

Q: 1. Given the functions fx) - x +1 and g(x) = -3- x, dete y = f(x) – g(x). y= x -x+2 b. y-x+x+4 a. 2.…

A:

Q: Suppose f is a linear function such that f(3) = 6 and f(7) = 1. Find the equation for f with respect…

A: Given,  f is a linear function such that f(3) = 6 and f(7) = 1

Q: In the following examples, some mistakes have occurred. Identify the mistakes and make corrections.

A: Given:

Q: 11. If f"(x)=-4sin 2.x, f(0)=0and f'(0) =2, find the value of f 4 %3D

A:

Q: Evaluate: g(f(-7)) y = f(x) y = g(x) 10 10 9. 8 6. 8. 7. 6. 6. 5. 4. 4. 3. 3 2. -10-9-8-7-6 -5 -4 -3…

A:

Q: Evaluate: f(g(6)) y = f(x) y = g(x) A10 10 8. 7. 4. 3 3 -1 -10-9-8 -7-6 -5 -4/-3 -2 -ı 1 2 3 4 5 6 7…

A: Given, The graph of fx  and gx We have to find fg6.

Q: 2] 20 Determine which value(s) are excluded from the domain and range of f(x): 4+x %3D X-3 Excluded…

A: fx=4+xx-3

Q: 1.) Let f(x) = 7 + What is f(3 + h)?

A:

Q: Evaluate: f(g(-1)) y = f(x) y = g(x) 10 4. +2 -10-9-8 -7 -6 -4 -3 -2 -!1 2 3 4 5 678 9 1o -10-9 -8…

A: First we will find the g(-1)from the graph y=g(x) then we will find the f(g(-1)) from the graph…

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)

Q: Based on the graphs of f(x) and g(x), what must the domain of (f. g)(x) be? 10 8 7 6 5 2 g(x) 1…

A:

Q: Let ​f(x)= 5x − ​1, ​h(x)= -x − 2.   Find ​(f◦​h)(−4​).

A:

Q: Evaluate: g(f(-3)) y fx) y = g(x) 10 10 6. 3 3456789 10 10-9-87-6 "5 -2 -1 2345678 9 10 -2 -4 to

A:

Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find 1. h[f(1)] 2.…

A: Given that f(x) = {(- 2, 1), (1, 4), (2, 5), (3, 6)} g(x) = 6 + 4x h(x) = - x 2 + 2 1. h[f(1)]/7 =…

Q: Evaluate: g(f(-7) y = f(x) y = g(x) 10 10 7. 6 4. 4. 3 1. -10-9--7 -6 -5 -4 -3 -2 - 1 2 3 4 5 67 8 9…

A: To find g(f(a)),  First we have to observe the value of f(x) at a from the graph of f(x) , lets say…

Q: Evaluate: g(f(7)) y = f(x) y = g(x) 10 10 9. 9. 7. 5. 4 3. 3. 2. 2. -10-9 -8-7 -6 - 4-3-2 -1 123 4 6…

A: GIVEN:-

Q: The critical points of the function f(x) 16x2 2x4 occur at - O x = = 0, x = ±1.60 x = 0, x = ±2.67 O…

A:

Q: Evaluate: f(g(-5)) y = f(x) y = g(x) 10 10 8 4 3. 2 -1 -10-9 -9-7 -6 -5 -4 -3 -2 -1N 1 2 3 4 5 6 7 8…

A: Consider the graph of f(x) and g(x)

Q: Consider f(x)=ax+xln(bx)f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x):…

A: f'(x)=a+1+logbx Increasing

Q: (2ł – 5) 7 (n² –5) For the function f(x) , find ƒ=1(x). - f- (x) = V (x + 5)° Of-'(x) = Væ5 + 5 O…

A:

Q: 1. Let f(x) = 2 + 13 f '(z) =

A: We have to use properties of inverse function here.

Q: Evaluate: g(f(2)) y = f(x) y = g(x) 10 10 9. 9 8 4 3 1 -1 -10-9-8-7-6-5-4 -3-2 -1 1 23 4 5 6 7 8 9…

A: Given that: Graph of g(x) and f(x) To calculate: g(f(2))

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: Find f ∘ g ∘ h. f(x) = x − 4,   g(x) =    x,   h(x) = x − 4

A: by composition of function.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.