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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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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

answer a 46
Answer : A) 46
  • g(2) = 3(2) + 1=7
  • f(7) = 72 – 3 = 46
slide9
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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