Functions Function Composition Amanda Bateman Def A function

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 y 2 = 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 defined ( )(x) = f(g(x)) • Given f(x) = 3 x and g(x) = 4 x + 2 what is • A) 12 x + 2 B) 12 x 2 + 6 x C) 12 x + 6 D) x + 2 • • • is

Answer : C) 12 x + 6 • Then f(4 x+2) = 3(4 x+2) = 12 x + 6

What is if f(x) = x 2 – 3 and g(x)= 3 x + 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) = 3 x + 2? y = 3 x + 2 (replace f(x) with y) x = 3 y + 2 (switch x and y) y= (solve for y) f-1(x) =