# Functions & Function Composition - PowerPoint PPT Presentation

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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

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

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

• A) 46

• B) 4

• C) 52

• D) 22

• 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) =

### 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)

• 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) =