Algebra Tutorials! Home 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 Â· g)(x) = f(x) Â· 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.