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Mathematics
Mathematics
Problem
Let
q
(
x
)
=
x
2
−
6
x
+
11
q(x)=x^{2}-6x+11
q
(
x
)
=
x
2
−
6
x
+
11
with
x
∈
R
x\in\mathbb{R}
x
∈
R
. a. (i) Identify an interval
I
I
I
on which
q
q
q
is one–one and justify your choice. b. (ii) For
x
∈
I
x\in I
x
∈
I
, find
q
−
1
(
x
)
q^{-1}(x)
q
−
1
(
x
)
in simplest form. c. (iii) Prove that
q
∘
q
−
1
=
Identity
q\circ q^{-1}=\text{Identity}
q
∘
q
−
1
=
Identity
on the appropriate set. d. (iv) Evaluate
q
−
1
(
7
)
q^{-1}(7)
q
−
1
(
7
)
.
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