OPERATIONS OF FUNCTIONhshdhsbdbbsbvvj.pdf
- 1. OPERATIONS OF FUNCTION MYLA M. ARONDA
- 2. OBJECTIVES A. define operation of functions. B. substitute each value in a given equation C. Perform the indicated operation
- 3. DEFINITION Let f and g be functions defined at a real number x. the sum, difference, product, and quotient functions f and g are the functions defined by (f + g)(x) = f(x) + g(x) sum function (f-g)(x) = f(x) – g(x) difference function (fg)(x) = f(x)g(x) product function , g(x) ≠ 0 quotient function
- 5. EXAMPLE Given thefunctions: 𝑓 (𝑥 )=𝑥 +5 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Find: (f + g)(x) (g+ h)(x)
- 6. Find (f + g)(x) Given: 𝑓 (𝑥 )=𝑥 +5 𝑔 (𝑥 )=2𝑥 −1 Solution: (f + g)(x) = f(x) + g(x) (f + g)(x) = (x + 5) + (2x-1) = x + 2x + 5 – 1 = 3x + 4 Definition of addition replace f(x) and g(x) by the given values. Combine like terms and perform the indicated values
- 7. Find (g + h)(x) Given: 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Solution: (g + h)(x) = g(x) + h(x) = (2x -1) + (2+9𝑥 −5 = 2 + 2x + 9x – 5 -1 = 2 + 11x -6 Definition of addition replace f(x) and g(x) by the given values. Combine like terms and perform the indicated values
- 9. EXAMPLE Given thefunctions: 𝑓 (𝑥 )=𝑥 +5 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Find: (f -g)(x) (g-h)(x)
- 10. Find: (f-g)(x) Given: 𝑓 (𝑥 )=𝑥 +5 𝑔 (𝑥 )=2𝑥 −1 Solution: (f – g)(x) = f(x) – g(x) = (x + 5) – (2x -1) = x + 5 -2x + 1 = x -2x + 5 + 1 = -x + 6 Definition of subtraction of functions replace f(x) and g(x) by the given values and given values and distribute the negative sign. combine like terms and perform the indicatedoperation
- 11. Find(g-h)(x) Given: 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Solution (g– h)(x) = g(x) – h(x) = (2x – 1) – (2+9𝑥 −5) = 2x - 1 -29𝑥 +5 = -2 - 9x + 2x +5 - 1 = -2 - 7x + 4 Definition of subtraction of functions replace f(x) and g(x) by the given values and given values and distribute the negative sign. combine like terms and perform the indicated operation
- 13. EXAMPLE Given the functions: f(x) = 2x -1 g(x) = + 1 h(x) = 3x - 4 Find: (gh) (x) (fh)(x)
- 14. Find: (gh) (x) Given: g(x) = + 1 h(x) = 3x -4 Solution (gh)(x) = g(x) • h(x) = + 1 ) (3x -4) = + 3x -4 - 4 = -4 + 3x - 4 Definition of multiplication of functions. Replace f(x0 and g(x) by the given values. Multiply the binomial
- 15. Find: (fh)(x) Given: f(x) = 2x -1 h(x) = 3x -4 Solution: (fh)(x) = f(x) • h(x) = (2x-1) (3x -4) = 6 - 3x – 8x + 4 = 6 - 11x + 4 Definition of multiplication of functions. Replace f(x0 and g(x) by the given values. Multiply the binomial
- 17. EXAMPLE Given thefunctions: 𝑓 (𝑥 )=𝑥 +5 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Find: (x)
- 18. Find: (x) GIVEN: 𝑔 (𝑥 )=2𝑥 −1 ℎ(𝑥 )=2+9𝑥 −5 Solution: (x) = = = = x + 5 Definition of division of functions replaceh(x) andg(x) by thegiven valuesfactor thenumerator cancel out thecommon factors.
- 19. Find: (x) Given: ℎ(𝑥 )=2+9𝑥 −5 𝑓 (𝑥 )=𝑥 +5 Solution: (x) = = = = 2x - 1 Definition of division of functions replaceh(x) andg(x) by thegiven valuesfactor thenumerator cancel out thecommon factors.