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Mathematics
Mathematics
Problem
1. a B is the image of A under a reflection in the line
y
=
x
y = x
y
=
x
. If A is
(
x
,
f
(
x
)
)
(x, f(x))
(
x
,
f
(
x
))
, find the coordinates of B. 2. b By substituting your result from a into
y
=
f
−
1
(
x
)
y = f^{-1}(x)
y
=
f
−
1
(
x
)
, show that
f
−
1
(
f
(
x
)
)
=
x
f^{-1}(f(x)) = x
f
−
1
(
f
(
x
))
=
x
. 3. c Using a similar method, show that
f
(
f
−
1
(
x
)
)
=
x
f(f^{-1}(x)) = x
f
(
f
−
1
(
x
))
=
x
.
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