1.5 Inverse
Functions
Properties, Domain and
Range
Goal
 You
should be able to determine the
inverse of linear functions and state their
properties.
Inverse Functions
The
reverse of the original function
Maps each output value back to the
corresponding input value
The "undo" of a function
Inverse Functions
The
inverse of a linear function is the
reverse of the original function.
It can be found by performing the
inverse operations (division instead of
multiplication, say) in reverse order.
f(x) = 2x – 3
f-1(x) = x + 3
2
Inverse Functions
It
can be found by exchanging the x
and y variables in the expression and
solving for y:
y = 5x + 8
(exchange x and y)
x = 5y + 8
y=x–8
5
Inverse Functions
The
inverse of a function is not
necessarily a function itself.
The inverse function of f(x) is written as
f-1(x).
If (a, b) is a point on the function y =
f(x) then (b, a) is a point on y = f-1(x).
Note: f-1(x) ≠ 1/f(x)
TOV
f(x)
f-1(x)
Mapping Diagrams
Graphing Inverse Functions
 When
graphing an inverse of a function, you
reflect it across the y = x line (as (x, y) of the
function is (y, x) of the inverse).
 Any points shared by both functions lie on y = x
and are called invariant points (shared by both
graphs)
Complete 1.5 notes worksheet
Domain and Range
 Given
the following function determine
the domain and range of both the function and its
inverse.
D
= {xЄR}, R = {f(x)ЄR}
 Inverse: x = -2(y+3)2 – 8
𝑥+8
−2

y=

D = {xЄR|x ≤ – 8} and R = {f-1(x)ЄR| f-1(x) ≥ – 3}
Note: when x = – 8, f-1(– 8) = – 3, f-1(– 10) = – 2

− 3 We know roots can’t be negative: when?
Class/Home work
 Pg
46 #1a, 2 – 4, 6, 7, 10, 12, 16, 17