**Problem Statement:**Find $(f \circ g)(x)$ when $f(x) = x^2 + 5x + 6$ and $g(x) = \frac{1}{x+3}$.**Options:**A. $\frac{5x^2 + 36x^2 + 81x + 55}{x^2 + 6x + 9}$B. $\frac{1}{x^2 + 5x + 9}$C. $x + 2$D. $\frac{6x^2 + 41x + 70}{x^2 + 6x + 9}$**Explanation of Subject Matter:**The problem presented involves function composition, where the output of one function $g(x)$ serves as the input for another function $f(x)$. This specific operation $(f \circ g)(x)$ requires substituting $g(x)$ into $f(x)$. Students need to work through this algebraic procedure to solve the problem correctly.**Additional Notes:**The question is part of an exam outlined in the title "8.2.1 - Test: Semester A Final Part 1," specific to "Sem 1 NC Math IV Part A." A progress meter shows that 8 out of 23 questions have been answered, which suggests this is a question within a broader series of math problems designed to evaluate students' knowledge and problem-solving skills in this context.

Answered: Image /qna-images/answer/6464b1a0-231e-45e2-98c4-7020fca65c88.jpg

Answered: 1 Find (fog)(x) when f(x)= x +5x+6 and…

1 Find (fog)(x) when f(x)= x +5x+6 and g(x) = x+3 O A. 5x+36x2+81x+55 2+6x+9 O B. 1 2+5x+9 O C. x+2 O D. 6x2 +41x+70 x2+6x+9

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Concept explainers

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.

Question

**Problem Statement:**

Find $(f \circ g)(x)$ when $f(x) = x^2 + 5x + 6$ and $g(x) = \frac{1}{x+3}$.

**Options:**

A. $\frac{5x^2 + 36x^2 + 81x + 55}{x^2 + 6x + 9}$

B. $\frac{1}{x^2 + 5x + 9}$

C. $x + 2$

D. $\frac{6x^2 + 41x + 70}{x^2 + 6x + 9}$

**Explanation of Subject Matter:**

The problem presented involves function composition, where the output of one function $g(x)$ serves as the input for another function $f(x)$. This specific operation $(f \circ g)(x)$ requires substituting $g(x)$ into $f(x)$. Students need to work through this algebraic procedure to solve the problem correctly.

**Additional Notes:**

The question is part of an exam outlined in the title "8.2.1 - Test: Semester A Final Part 1," specific to "Sem 1 NC Math IV Part A." A progress meter shows that 8 out of 23 questions have been answered, which suggests this is a question within a broader series of math problems designed to evaluate students' knowledge and problem-solving skills in this context.

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