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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
Powers
Solving Quadratic Equations by Completing the Square
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Functions

Operations With Functions

Operations Symbols
Addition (f + g)(x) = f(x) + g(x)
Subtraction (f - g)(x) = f(x) - g(x)
Multiplication (f · g)(x) = f(x) · g(x)
Division

The domain of the sum, difference and product of f and g consist of all real numbers for which f and g are defined. The domain of the quotient of f and g consists of all real numbers for which f and g are defined and g 0.

 

Composition of Functions

Definition: The composite function, f of g, is denoted by f g and defined by (f o g)(x) = f(g(x)).

The domain of f o g is the subset of the domain of g for which f g is defined.

The composite function g o f is defined by (g o f)(x) = g(f(x).

The domain of g o f is the subset of the domain of f for which g o f is defined.

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