1.5 Inverse Functions
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Transcript 1.5 Inverse Functions
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