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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
ln
(
x
2
−
1
x
+
2
)
,
x
≠
±
1
,
x
≠
−
2.
f(x)=\ln\left(\frac{x^2-1}{x+2}\right), \quad x\neq\pm1,\;x\neq-2.
f
(
x
)
=
ln
(
x
+
2
x
2
−
1
)
,
x
=
±
1
,
x
=
−
2.
(i) Determine the domain of
f
f
f
in the set of real numbers. (ii) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
and simplify the expression as far as possible. (iii) Evaluate
f
′
(
3
)
f'(3)
f
′
(
3
)
.
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