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## PowerPoint Slideshow about ' Functions & Function Composition' - warren

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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

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

- A) 46
- B) 4
- C) 52
- D) 22

Answer : A) 46

- 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)

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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