x, - X₂ 5. If f(x,) – f(xx) = f 1 - X,X2 is f(x) equal to? 1-x 1+x for X1, X2 € (-1, 1), then what [2016-1] 2+x Х (a) In (b) In 1-X 1-x 1+x x -1 tan - 1 (C) c (d) tan 1+x 1-X 2
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Step-by-step explanation:
Correct option is
A
log(
1+x
1−x
)
B
tan
−1
(
1+x
1−x
)
C
log(
1−x
1+x
)
When x
1
=−1 and x
2
=1, then
f(−1)−f(1)=f(
1−1(1)
−1−1
)=f(−1)⇒f(1)=0
which is satisfied when f(x)=tan
−1
(
1+x
1−x
)
when x
1
=x
2
=0, then
f(0)−f(0)=f(
1−0
0−0
)=f(0)⇒f(0)=0
when x
1
=−1 and x
2
=0, then
f(−1)−f(0)=f(
1−0
−1−0
)=f(−1)⇒f(0)=0
which is satisfied when f(x)=log(
1+x
1−x
) and f(x)=log(
1−x
1+x
)
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