Given, f(x) = l o g 1 + x 1 − x and g(x) = 3 x + x 3 1 + 3 x 2 then (fog) (x) equals Options: A . &nbsp-f(x) B . &nbsp3f(x) C . &nbsp[f(x)]3 D . &nbspNone of these

Answer: Option B : B ( f o g ) ( x ) = f ( g ( x ) ) = f ( 3 x + x 3 1 + 3 x 2 ) = l o g 1 + 3 x 2 + 3 x + x 3 1 + 3 x 2 − 3 x − x 3 = l o g ( 1 + x ) 3 ( 1 − x ) 3 = 3 f ( x )

Given, f(x) = log1+x1−x and g(x) =3x+x31+3x2 then (fog) (x) equals

Question

Given, f(x) =

l o g \frac{1 + x}{1 - x}

and g(x)

= \frac{3 x + x^{3}}{1 + 3 x^{2}}

then (fog) (x) equals

Options:

A . -f(x)

B . 3f(x)

C . [f(x)]3

D . None of these

Answer: Option B
:
B

(f o g) (x) = f (g (x)) = f (\frac{3 x + x^{3}}{1 + 3 x^{2}}) = l o g \frac{1 + 3 x^{2} + 3 x + x^{3}}{1 + 3 x^{2} - 3 x - x^{3}} = l o g \frac{(1 + x)^{3}}{(1 - x)^{3}} = 3 f (x)

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