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# Solutions for Chapter 10-1: COMPOSITION OF FUNCTIONS

## Full solutions for Functions Modeling Change: A Preparation for Calculus | 4th Edition

ISBN: 9780470484753

Solutions for Chapter 10-1: COMPOSITION OF FUNCTIONS

Solutions for Chapter 10-1
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##### ISBN: 9780470484753

Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753. This textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10-1: COMPOSITION OF FUNCTIONS includes 65 full step-by-step solutions. Since 65 problems in chapter 10-1: COMPOSITION OF FUNCTIONS have been answered, more than 26120 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Bounded above

A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

• Circle

A set of points in a plane equally distant from a fixed point called the center

• Complex number

An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

• Conjugate axis of a hyperbola

The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

• Damping factor

The factor Ae-a in an equation such as y = Ae-at cos bt

• Difference of two vectors

<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>

• Division

a b = aa 1 b b, b Z 0

• Imaginary axis

See Complex plane.

• Inverse cosecant function

The function y = csc-1 x

• Lower bound of f

Any number b for which b < ƒ(x) for all x in the domain of ƒ

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• Matrix element

Any of the real numbers in a matrix

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

• Relevant domain

The portion of the domain applicable to the situation being modeled.

• Root of an equation

A solution.

• Secant

The function y = sec x.

• Solution of an equation or inequality

A value of the variable (or values of the variables) for which the equation or inequality is true

• Spiral of Archimedes

The graph of the polar curve.

• Zero matrix

A matrix consisting entirely of zeros.

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