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Mathematics
Mathematics
Problem
For the parameter
a
∈
R
a\in\mathbb{R}
a
∈
R
, define
f
a
(
x
)
=
x
+
a
f_a(x)=\sqrt{x+a}
f
a
(
x
)
=
x
+
a
and
g
(
t
)
=
1
t
−
2
g(t)=\dfrac{1}{t-2}
g
(
t
)
=
t
−
2
1
. (i) Determine all real values of
a
a
a
for which
(
g
∘
f
a
)
(
x
)
(g\circ f_a)(x)
(
g
∘
f
a
)
(
x
)
is defined for at least one real
x
x
x
. (ii) For
a
=
3
a=3
a
=
3
, find the domain of
(
g
∘
f
a
)
(
x
)
(g\circ f_a)(x)
(
g
∘
f
a
)
(
x
)
.
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