3. DEFINITION OF INVERSES
Two
functions f and g are inverses if:
f(g(x)) = x and g(f(x)) = x
To
check if two functions are inverses,
perform both compositions and make
sure both equal x.
7. FINDING INVERSES
graph of f -1 is the reflection of f
over the line y = x
Can be found by
switching x and y
in the ordered pairs.
Find equation of f -1
by switching x and y
in the equation and
solving for y.
The
8. EXAMPLE 2
f(x) = 4 – x2 for x 0.
Sketch the graph of f and f -1 (x)
Find a rule for f -1 (x)
Let
9. YOU TRY!
g(x) = (x – 4)2 – 1 for x 4.
Sketch the graph of g and g -1 (x)
Find a rule for g -1 (x)
Let
12. DO ALL FUNCTIONS HAVE
INVERSES?
the graph of y = x2 over the
line y = x.
Is the result a function?
Reflect
13. ONE-TO-ONE
Only
functions that are one-to-one
have inverses.
One-to-one means each x value has
exactly one y value and each y has
exactly one x
Can check using horizontal line test.