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Mathematics
Problem
Consider the functions
f
(
x
)
=
3
x
−
2
f(x)=3x-2
f
(
x
)
=
3
x
−
2
and
g
(
t
)
=
5
−
t
g(t)=\sqrt{5-t}
g
(
t
)
=
5
−
t
. (a) Find the domain of the composite function
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
. (b) Hence evaluate
(
g
∘
f
)
(
1
)
(g\circ f)(1)
(
g
∘
f
)
(
1
)
, showing that the ordered pair obtained lies in the range of
g
g
g
.
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