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Mathematics
Mathematics
Problem
If
f
(
x
)
=
sin
−
1
1
+
x
2
−
1
2
1
+
x
2
f(x)=\sin^{-1}\sqrt{\frac{\sqrt{1+x^2}-1}{2\sqrt{1+x^2}}}
f
(
x
)
=
sin
−
1
2
1
+
x
2
1
+
x
2
−
1
, then which of the following is (are) correct? (a)
f
′
(
−
1
)
=
−
1
4
f'(-1)=\frac{-1}{4}
f
′
(
−
1
)
=
4
−
1
(b)
f
′
(
1
)
=
1
4
f'(1)=\frac{1}{4}
f
′
(
1
)
=
4
1
(c)
f
(
x
)
f(x)
f
(
x
)
is an odd function (d)
f
(
x
)
f(x)
f
(
x
)
is an even function
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