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Mathematics
Mathematics
Problem
Let
p
(
x
)
=
4
(
1
3
)
x
p(x)=4\left(\dfrac{1}{3}\right)^{x}
p
(
x
)
=
4
(
3
1
)
x
. a. (i) Find the exact value of
p
(
3
2
)
p\left(\dfrac{3}{2}\right)
p
(
2
3
)
. b. (ii) Compute
p
(
−
2
)
p(-2)
p
(
−
2
)
. c. (iii) Simplify the ratio
p
(
−
2
)
p
(
3
2
)
\dfrac{p(-2)}{p\left(\dfrac{3}{2}\right)}
p
(
2
3
)
p
(
−
2
)
and express your answer as a single power of
3
3
3
. d. (iv) Prove that for any real number
x
x
x
,
p
(
x
+
1
)
=
1
3
p
(
x
)
p(x+1)=\dfrac{1}{3}\,p(x)
p
(
x
+
1
)
=
3
1
p
(
x
)
.
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