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Mathematics
Mathematics
Problem
Define
q
(
x
)
=
⌊
∣
3
x
−
4
∣
2
⌋
×
sgn
(
1
−
x
)
q(x)=\left\lfloor \dfrac{|3x-4|}{2} \right\rfloor \times \operatorname{sgn}(1-x)
q
(
x
)
=
⌊
2
∣3
x
−
4∣
⌋
×
sgn
(
1
−
x
)
. a. (i) Find
q
(
−
1
)
q(-1)
q
(
−
1
)
. b. (ii) Find
q
(
1
)
q(1)
q
(
1
)
. c. (iii) Find
q
(
4
3
)
q\!\left(\dfrac{4}{3}\right)
q
(
3
4
)
. d. (iv) Hence obtain the product
q
(
−
1
)
q
(
1
)
q
(
4
3
)
q(-1)\,q(1)\,q\!\left(\dfrac{4}{3}\right)
q
(
−
1
)
q
(
1
)
q
(
3
4
)
.}],
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