2x If f(x) = log 1+x 1-x then f is equal to 9 1 + x2​

Question

2x
If f(x) = log
1+x
1-x
then f
is equal to
9
1 + x2​

in progress 0
Charlie 3 months 2021-11-10T16:55:40+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-10T16:57:14+00:00

    Answer:

    keep smiling….

    Step-by-step explanation:

    f(x) = ln (1-x/1+x)

    Given that f(x) +f (y) = f(x+y /1 +xy)

    ln (1-x/1+x) + ln (1-y/1+y) = ln (1 -(x+y)/1 +x+y)

    ln((1-x)× (1-y)/(1+x)× (1+y)) = ln (1-(x+y)/1+x+y)

    Removing log

    And. Then on solving

    We get

    2xy(x+y) = 0

    Hence xy = 0 or x+y = 0

    For xy = 0, solution is but obvious

    For x+y = 0, x = -y

    Putting in the given equation

    ln((1+x)× (1-x)/(1-x)(1+x)) = ln1

    LHS and RHS contradicts

    Hence

    x = 0 = y

    Also

    1-x >0

    x 1

    hence x belongs to (0, 1)…….

    ================

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