Given f x -log1- x -1- x and g x -3 x - x 3-1-3 x 2 then fog x equalsA- -fxB- 3 fx - -fx-3D- 2 fx

The correct option is B f(x)=log ( 1+x/1 x ) and g(x)=3x+x^3/1+3x^2 fog(x)=f(g(x))= (3x+x^3/1+3x^2 )=log ( 1+3x+x^3/1+3x^2/1 3x+x^3/1+3x^2 ) =log ( 1+3x+3x+x ...

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Byju's Answer

Standard XI

Mathematics

Arithmetic Progression

Given f x =lo...

Question

Given $f (x) = l o g (\frac{1 + x}{1 - x}) a n d g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$ then fog (x) equals

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Solution

The correct option is B
$f (x) = l o g (\frac{1 + x}{1 - x}) a n d g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$
$f o g (x) = f (g (x)) = (\frac{3 x + x^{3}}{1 + 3 x^{2}}) = l o g ⎛ ⎜ ⎝ \frac{1 + \frac{3 x + x^{3}}{1 + 3 x^{2}}}{1 - \frac{3 x + x^{3}}{1 + 3 x^{2}}} ⎞ ⎟ ⎠$
= $l o g (\frac{1 + 3 x + 3 x + x^{3}}{1 + 3 x - 3 x - x^{3}}) = l o g (\frac{(1 + x)^{3}}{(1 - x)^{3}})$
$l o g (1 + x)^{3} - l o g (1 - x)^{3}$
= $3 l o g (1 + x) - 3 l o g (1 - x)$
= $3 l o g (\frac{1 + x}{1 - x}) = 3 f (x)$

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Given f(x)=log(1+x1−x) and g(x)=3x+x31+3x2 then fog (x) equals

The correct option is B f(x)=log(1+x1−x) and g(x)=3x+x31+3x2 fog(x)=f(g(x))=(3x+x31+3x2)=log⎛⎜⎝1+3x+x31+3x21−3x+x31+3x2⎞⎟⎠ =log(1+3x+3x+x31+3x−3x−x3)=log((1+x)3(1−x)3) log(1+x)3−log(1−x)3 =3log(1+x)−3log(1−x) =3log(1+x1−x)=3f(x)

Given $f (x) = l o g (\frac{1 + x}{1 - x}) a n d g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$ then fog (x) equals