Functions function composition
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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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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

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.


Is y 2 x a function

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


Functions can be added subtracted multiplied or divided to form new functions

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) =


Def the composite function is defined x f g x

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


Answer c 12x 6

Answer : C) 12x + 6

  • Then f(4x+2) = 3(4x+2)

    = 12x + 6


What is if f x x 2 3 and g x 3x 1

What is if f(x) = x2 – 3 and g(x)= 3x + 1?

  • A) 46

  • B) 4

  • C) 52

  • D) 22


Answer a 46

Answer : A) 46

  • g(2) = 3(2) + 1=7

  • f(7) = 72 – 3 = 46


Functions function composition

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) =


Two functions f g are inverses of one another if and

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)


Answer d

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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