3. Functions

Use the definition of inverses to determine whether ƒ and g are inverses. f(x) = 2/(x+6), g(x) = (6x+2)/x

Use the definition of inverses to determine whether ƒ and g are inverses. f(x) = x²+3, x≥0; g(x) = √x-3, x≥3

Determine whether the given functions are inverses.

Determine whether the given functions are inverses. ƒ= {(2,5), (3,5), (4,5)}; g = {(5,2)}

Find the inverse of each function that is one-to-one. {(3,-1), (5,0), (0,5), (4, 2/3)}

Find the inverse of each function that is one-to-one. {(1, -3), (2, -7), (4, -3), (5, -5)}

Determine whether each pair of functions graphed are inverses.

Determine whether each pair of functions graphed are inverses.

Determine whether each pair of functions graphed are inverses.

Determine whether each pair of functions graphed are inverses.

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=3x+8 and g(x) = (x-8)/3

The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = 1/x

Which graphs in Exercises 29–34 represent functions that have inverse functions?

Which graphs in Exercises 29–34 represent functions that have inverse functions?

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of f and ƒ¯¹. f(x)=2x-1