College Algebra Quiz
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FUNCTIONS & GRAPHS
Question 1
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The inverse function
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
exists for
f
(
x
)
=
x
+
3
−
2
f(x) = \sqrt{x+3} - 2
f
(
x
)
=
x
+
3
−
2
with domain
[
−
3
,
∞
)
[-3, \infty)
[
−
3
,
∞
)
. If
g
(
x
)
=
[
f
−
1
(
x
)
]
2
+
1
g(x) = [f^{-1}(x)]^2 + 1
g
(
x
)
=
[
f
−
1
(
x
)
]
2
+
1
, what is the domain of
g
(
x
)
g(x)
g
(
x
)
?
A
(
−
∞
,
∞
)
(-\infty, \infty)
(
−
∞
,
∞
)
because squaring the inverse function eliminates all domain restrictions
B
[
−
3
,
∞
)
[-3, \infty)
[
−
3
,
∞
)
because
g
(
x
)
g(x)
g
(
x
)
inherits the same domain restrictions as
f
(
x
)
f(x)
f
(
x
)
C
[
1
,
∞
)
[1, \infty)
[
1
,
∞
)
because
g
(
x
)
g(x)
g
(
x
)
squares the inverse function and adds 1, shifting the minimum value
D
[
−
2
,
∞
)
[-2, \infty)
[
−
2
,
∞
)
because this represents the range of the original function
f
(
x
)
f(x)
f
(
x
)
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