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(Section 1.9: Inverses of OnetoOne Functions)
1.9.12
Step 3
: Solve for
y
.
7
x
=
y
3
+
5
Multiplied both sides by 7
()
7
x
±
5
=
y
3
Subtracted 5 from both sides
7
x
±
5
3
=
y
Cubed both sides
WARNING 3
:
Squaring
both sides of an equation may or
may not yield an equivalent equation.
y
=
7
x
±
5
3
• Compare these steps with Steps 3*, 2*, and 1* in Example 6.
Step 4
: Replace
y
with
f
±
1
x
, if we obtain a function.
f
±
1
x
=
7
x
±
5
3
•
f
±
1
is a function, because
f
was
onetoone
.
Step 5
: If necessary, impose restrictions and ensure that
Dom
f
=
Range
f
±
1
, and
Dom
f
±
1
=
Range
f
.
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 Spring '09

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