Functions &amp; Function Composition

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# Functions & Function Composition - PowerPoint PPT Presentation

Functions &amp; 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

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

• 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 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:
• (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))
• 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
• Then f(4x+2) = 3(4x+2)

= 12x + 6

• g(2) = 3(2) + 1=7
• f(7) = 72 – 3 = 46
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) =

If f(x) = 3x + 2 and g(f(x)) = x then what does g(x)=?

A) 3x – 2

B) 3x

C)

D)