Transcript No Slide Title

Lora Santucci
Mathematics department consulting teacher
Morris Hills High School
Morris Hills Regional School district
Rockaway, NJ
[email protected]
How are inverse functions traditionally taught?
What is the best way to help students understand inverses?
How can the idea of an inverse be connected
to other concepts in students’ mathematical knowledge?
What can we do to give students a more active role
in learning mathematics?
List steps to get up and out
List what you do to go to bed
How does the second process
compare to the first?
Inverses UNDO eachother
(x,y) is on f
What point must
be on
f
-1 (“f-inverse”)
(y, x)
must be on
f
-1
CHECK
f ( f -1 (x))
and
f -1( f (x))
Both should equal x
Because inverses
“undo” eachother!
To find f
-1
1. SWITCH x and y
2. Solve
3. Call it f
-1 (x)
Example: y = 2 x +8
STEP 1
x=2y+8
x  2y 8
x 8  2y
 x  8  y
2
3. Call it f
f
1
-1 &
check
x  8

( x) 
2
Find the inverse of
3x  2
f ( x) 
x 1
Find the inverse of
f (x) =
2
x
–3
Find the inverse of
f (x) = 2(x – 3
2
)
+5