Let f(x) = 11x and g(x) = 7x73. Find (fg) (x) and (x). Then evaluate fg and for x = -8. %3D (fg)(x) = : (fg)(-8) = O %3D (x) = -8) State the domain of (fg)(x) and The domain of (/g)(x) is and the domain of (2)(x) is

Q: Given f(x) = x² + 3x + 9, find the following. HINT %3D (a) f(0) (b) f(1) (c) f(-1) (d) f(-3) (e)…

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Q: What is the vertex of the function f(x) = 19(x+6)2 %3D O (19, 6) O (6, 19) O (6, 0) O (6, 0)

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Q: Find f(x) g(x) = (fg)(x). Simplify. f(x) = x2 + 2 %3D g(x) = x2 - x + 9

A: Given, f(x) = x2+2 g(x) = x2-x+9

Q: 5x3 + 6x2 + 2, f (0) 3 and f(1) -2. %3D 15. Find f for f"(x)

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Q: Let f(x) =x²-x -5 and gx)= -8x+4. Find g(3) and f(g(3)). %3D 9(3) = f(g(3)) = %3D %3D

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Q: Let f(x) = V2 - x+ 8. Determine f-(x) and the the domain of f(z). f(x) = %3D Domain of f-(æ) =

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Q: (4x +7)(5– 2x) f(x)= %3D (x-1)²

A: Given data:     The expression for the function is: f(x)=(4x+7)(5-2x)/(x-1)2.   The expression for…

Q: If we want to prove by contradiction the statement: For any positive real number x there exists a…

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Q: Let f(x) = - 9x + 12 and g(x) = x2 + 6. %3D Find f(5) + g(5).

A: Given that f(x)=-9x+12.       and g(x)=x2 + 6 find f(5)+g(5)

Q: 8x2

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Q: If f(x) = x² + 5 and g(x) = x – 4, evaluate the following %3D f(6) a. b. g(6)

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Q: Let f(x) = 2- 4x + 11x. Calculate the following values: %3D f(a) = f(a + h) = f(a + h) - f(a) | for…

A: We use identity  (a+b)2= a2+b2+2ab

Q: Use the functions, f (x) = 2x + 3 and g(x) = –x² + 5x and h(x) = x + 4 to find f (g(h(x))). %3D %3D

A: Given : f(x) = 2x + 3g(x) = -x2 + 5xh(x) = x + 4

Q: Let f(x) = 5x +1 and g(x) = X-1 Simplify the expressions f g g(f(4)), and g(f(x)). ...... g(f(4)) =…

A: The objective of the question is simplify the composition function at given point.

Q: Let f(x) = - 9x + 20 and g(x) = x² + 8. Find f(- 5) • g(- 5). f(- 5) • g(- 5) =

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Q: Let f(x) = -3x² and g(x) = 2x – 6. Find and simplify_the following. | g(f(x)) = b. f(g(x)) =

A: f(x)=-3x2, g(x)=2x-6a) g(f(x))=g(-3x2)=2(-3x2)-6=-6x2-6g(f(x))=-6x2-6

Q: Evaluate the indicated function for f(x) = x2 + 1 and g(x) (f + g)(t - 5) = x - 3. %3D (f + g)(t –…

A: First find the addition of the function (f + g) (x):

Q: Let f(x) and g(x) = 2x +9. %3D Then (fo g)(1) (f o g)(x) %3D

A: Substitute g(x) for x in f(x) to get (f o g)(x). This also means: (f o g)(x) = f[g(x)] Substitute…

Q: Var(X) = Var(Y) = 10.  If X and Y are independent - calculate the value of Var(0.6X + 0.4Y + 10).

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: Q2. Let S(x) = (x+2), and g(x)= (x+) gof and fog find

A: From the given data:

Q: Which function is equivalent to h(z) = = 9x - 24 + 16? Oh(z) (9z - - 4) 4) (x – 4) Oh(z) (9x + 4) (x…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.