22 terms

relation

any set of ordered pairs, a pairing of input (x) values and output (y) values

domain

the set of all the input values

range

the set of all output values

inverse relation

changes the input (domain) and the output (range) values of the original relation

domain switches w/

range

range switches w/

domain

the graph of an original relation is always a _______ of the graph of the original equation over line y=x

reflection

over what line is an inverse relation reflected on

y=x

how many steps to FINDING the inverse of an equation?

2

step #1 (finding the inverse of an equation)

rewrite the equation switching x and y

step #2 (finding the inverse of an equation)

isolate (solve) for y

both the original relation and its inverse are functions ....

only in some cases

f and g are inverses if and only if

f ( g (x) ) = g ( f (x) ) = x

reciprocals are also what?

multiplicative inverses

+, - and X, / are examples of what

inverse operations

what is inverse?

undoing

when graphing, what do you do with your table when graphing the inverse function

reverse it

notation for the inverse of f(x)

f^-1(x)

how is f^-1(x) read as

f inverse of x

what do you use when VERIFYING that the functions are inverses

f ( g (x) = g ( f (x) ) = x

what do we use when determing if an original function has an inverse that is also a fucntion

horizontal line test

every function has an _______, but not every inverse will be a _______!

inverse; function