Thread: Functions...

1) How can a graph be used to find the inverse of a function?

2) Do all functions have inverses? (I believe the answer is yes, but they are not necessarily functions)

3) What does it mean for two functions to be inverse of each other?

4) How can you use algebra to determine if an inverse function exists?

5) How can you determine if an inverse function exists when given a graph of a function?

Originally Posted by realintegerz

1) How can a graph be used to find the inverse of a function?

reflect the function in the line y = x to get the inverse function

2) Do all functions have inverses? (I believe the answer is yes, but they are not necessarily functions)

no

if they are not necessarily functions it would mean that an inverse function does not always exist, right?

3) What does it mean for two functions to be inverse of each other?

if f(x) and g(x) are real valued functions that are inverses of each other, then f(g(x)) = g(f(x)) = x

4) How can you use algebra to determine if an inverse function exists?

switch x and y and solve for y

5) How can you determine if an inverse function exists when given a graph of a function?

check if it is one-to-one and onto


do you know what the inverse function does?

all this is information you could easily find by doing a web-search, by the way

what do you mean check one to one and onto?

Originally Posted by realintegerz

what do you mean check one to one and onto?

Use horizontal line test to see if it one to one