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Mathematics
Mathematics
Problem
Let
f
t
:
R
→
R
f_t: \mathbb R \to \mathbb R
f
t
:
R
→
R
be defined by
f
t
(
x
)
=
t
x
+
5
f_t(x)=tx+5
f
t
(
x
)
=
t
x
+
5
, where
t
∈
R
t\in\mathbb R
t
∈
R
. a. (i) Determine the value(s) of
t
t
t
for which
f
t
f_t
f
t
is a bijection. b. (ii) For those value(s) of
t
t
t
, find
f
t
−
1
(
x
)
f_t^{-1}(x)
f
t
−
1
(
x
)
.
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