22 terms

algebra II inverse functions

STUDY
PLAY
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