Lesson 2: Operations on Functions PDF
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This document is a lesson on operations on functions in general mathematics. It provides examples of evaluating functions and performing operations like addition and subtraction on functions. It also describes steps for solving such problems, covering rules of exponents and other mathematical concepts in this domain.
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LESSON 2 GENERAL MATHEMATICS Performs addition, subtraction, multiplication, and division, of functions. EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3....
LESSON 2 GENERAL MATHEMATICS Performs addition, subtraction, multiplication, and division, of functions. EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 𝑓 𝑥 = 2𝑥 + 1 𝑓 𝑥 = 2(3) + 1 𝑓 𝑥 =6+1 𝒇 𝒙 =𝟕 EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 2 𝑞 𝑥 = 𝑥 − 2𝑥 + 2 2 𝑞 𝑥 = (3) −2(3) + 2 𝑞 𝑥 =9−6+2 𝒒 𝒙 =𝟏 EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 2 𝑓 𝑥 = 𝑥 + 3𝑥 + 9 2 𝑓 𝑥 = (3) +3(3) + 9 𝑓 𝑥 =9+9+9 𝒇 𝒙 = 𝟐𝟕 STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms. EXAMPLES 1. f(x) = 2𝑥 − 5𝑥 + 4 ; 3 g(x) = 3𝑥 + 2𝑥 − 6 2 2. f(x) = 2𝑥 − 1 ; g(x) = 𝑥 + 𝑥 − 2 2 EXAMPLE: 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 ; 3 2 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝒇+𝒈 𝒙 =𝒇 𝒙 +𝒈 𝒙 3 2 𝒇 + 𝒈 𝒙 = (2𝑥 −5𝑥 + 4) + (3𝑥 +2𝑥 − 6) 3 2 𝒇 + 𝒈 𝒙 = 2𝑥 +3𝑥 −5𝑥 + 2𝑥 + 4 − 6 𝟑 𝟐 𝒇 + 𝒈 𝒙 = 𝟐𝒙 +𝟑𝒙 −𝟑𝒙 − 𝟐 STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms. EXAMPLE: 2. 𝑓(𝑥) = 2𝑥 − 1 ; 2 𝑔 𝑥 =𝑥 +𝑥 −2 𝒇+𝒈 𝒙 =𝒇 𝒙 +𝒈 𝒙 2 𝒇 + 𝒈 𝒙 = (2𝑥 − 1) + (𝑥 +𝑥 − 2) 2 𝒇 + 𝒈 𝒙 = 𝑥 + 2𝑥 + 𝑥 − 1 − 2 𝟐 𝒇 + 𝒈 𝒙 = 𝒙 + 𝟑𝒙 − 𝟑 STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms. STEPS 1. Substitute the value of the 2 functions. 2. Change the sign of the subtrahend 3. Combine like terms. EXAMPLES 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 3 2. 𝑓(𝑥) = 2𝑥 − 1 ; 2 2 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝑔(𝑥) = 𝑥 + 𝑥 − 2 EXAMPLES STEPS 1. Substitute the value of the 2 functions. 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 ; 3 2. Change the sign of the subtrahend. 2 3. Combine like terms. 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝒇−𝒈 𝒙 =𝒇 𝒙 −𝒈 𝒙 𝒇−𝒈 𝒙 3 2 = 2𝑥 − 5𝑥 + 4 − (3𝑥 +2𝑥 − 6) 3 2 𝒇−𝒈 𝒙 = 2𝑥 − 5𝑥 + 4 + (−3𝑥 −2𝑥 + 6) 3 2 𝒇−𝒈 𝒙 = 2𝑥 −3𝑥 −5𝑥 − 2𝑥 + 4 + 6 𝟑 𝟐 𝒇 − 𝒈 𝒙 = 𝟐𝒙 −𝟑𝒙 −𝟕𝒙 + 𝟏𝟎 EXAMPLES STEPS 1. Substitute the value of the 2 functions. 2.𝑓(𝑥) = 2𝑥 − 1; 2. Change the sign of the subtrahend. 2 3. Combine like terms. 𝑔(𝑥) = 𝑥 + 𝑥 − 2 𝒇−𝒈 𝒙 =𝒇 𝒙 −𝒈 𝒙 𝒇−𝒈 𝒙 2 = 2𝑥 − 1 − (𝑥 +𝑥 − 2) 2 𝒇−𝒈 𝒙 = 2𝑥 − 1 + (−𝑥 −𝑥 + 2) 2 𝒇−𝒈 𝒙 = −𝑥 + 2𝑥 − 𝑥 − 1 + 2 𝟐 𝒇 − 𝒈 𝒙 = −𝒙 + 𝒙 + 𝟐 LAWS OF EXPONENT 𝑚 𝑛 𝑚+𝑛 1. Product rule; 𝑥. 𝑥 = 𝑥 𝑚 𝑛 𝑚.𝑛 2. Power rule; (𝑥 ) =𝑥 𝑛 𝑛 𝑛 3. Power of product; (𝑥𝑦) = 𝑥 𝑦 EXAMPLES 1. Multiplying a binomial to a monomial. f(x) = 5𝑥 g(x) = 𝑥 + 4 2. Multiplying a binomial to a binomial (FOIL METHOD) f(x) = 𝑥 + 3 g(x) = 𝑥 + 5 3. Multiplying a binomial to a trinomial f(x) = 9𝑥 − 5 g(x) = 6𝑥 + 𝑥 − 7 2 RULES OF DIVISION OF EXPONENT 𝑥𝑚 ; 𝑥 5 2 1. 𝑛 = 𝑥 𝑚−𝑛 = 𝑥 5−3 = 𝑥 𝑥 𝑥3 2. 𝑛 = 𝑤ℎ𝑒𝑛 𝑚 < 𝑛; 6 = 2 𝑥 𝑚 𝑥 4 1 𝑥 𝑥 𝑥 0 3. 𝑥 = 1 EXAMPLES 1. f(x) = 15 𝑥 15 2. f(x) = −4 𝑥 5 3. f(x) = 9 𝑥6 g(x) = 3 𝑥 9 g(x) = 2𝑥 8 g(x) = 9 𝑥 6