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Functions & Function Composition

Functions & Function Composition. Amanda Bateman. Def: A function is any process that assigns a single value of y to each number of x. Because x determines the value of y: y is the dependent variable x is the independent variable

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Functions & Function Composition

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  1. Functions & Function Composition Amanda Bateman

  2. Def: A function is any process that assigns a single value of y to each number of x. • Because x determines the value of y: y is the dependent variable x is the independent variable • The set of x values by which the function is defined is called the domain. • The set of corresponding values of y is called the range.

  3. Is y2 = x a function? • Solve for y to get • y = +√x or -√x • Thus for x = 1 you get y = 1, -1 • Not a function

  4. Functions can be added, subtracted, multiplied or divided to form new functions: • (f+g)(x) = f(x) + g(x) • (f-g)(x) = f(x) – g(x) • (fg)(x) = f(x)g(x) • (f/g)(x) =

  5. Def: The composite function is defined ( )(x) = f(g(x)) • Given f(x) = 3x and g(x) = 4x + 2 what is • A) 12x + 2 • B) 12x2 + 6x • C) 12x + 6 • D) x + 2

  6. Answer : C) 12x + 6 • Then f(4x+2) = 3(4x+2) = 12x + 6

  7. What is if f(x) = x2 – 3 and g(x)= 3x + 1? • A) 46 • B) 4 • C) 52 • D) 22

  8. Answer : A) 46 • g(2) = 3(2) + 1=7 • f(7) = 72 – 3 = 46

  9. Def : The inverse of a function, f-1, is obtained from f by interchanging the x and the y and then solving for y. What is the inverse of f(x) = 3x + 2? y = 3x + 2 (replace f(x) with y) x = 3y + 2 (switch x and y) y = (solve for y) f-1(x) =

  10. Two functions f & g are inverses of one another if and . If f(x) = 3x + 2 and g(f(x)) = x then what does g(x)=? A) 3x – 2 B) 3x C) D)

  11. Answer : D) • First solve f(x) = y = 3x + 2 for x • So you get x = • Then switch x and y to get y = • Then replace y with g(x) to get g(x) =

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