Restrict Domain to Make Invertible
Algebra · Flashcards · Application
ALGEBRA · FLASHCARDS
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QUESTION
What is the range of
f
(
x
)
=
−
(
x
+
2
)
2
f(x)=-(x+2)^2
f
(
x
)
=
−
(
x
+
2
)
2
when the domain is restricted to
x
≥
−
2
x\ge -2
x
≥
−
2
?
QUESTION
What is
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
for
f
(
x
)
=
x
2
−
4
f(x)=x^2-4
f
(
x
)
=
x
2
−
4
with restricted domain
x
≤
0
x\le 0
x
≤
0
?
QUESTION
What is
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
for
f
(
x
)
=
x
2
−
4
f(x)=x^2-4
f
(
x
)
=
x
2
−
4
with restricted domain
x
≥
0
x\ge 0
x
≥
0
?
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ANSWER
f
−
1
(
x
)
=
x
+
4
f^{-1}(x)=\sqrt{x+4}
f
−
1
(
x
)
=
x
+
4
. Solve
y
=
x
2
−
4
y=x^2-4
y
=
x
2
−
4
for
x
x
x
using the positive square root.
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