If fx-log1-x-1-x and gx-3 x-x3-1-3 x2- then fgx is equal to

3f(x) f(x) = log ( 1+x/1 x ) and g(x) = 3x+x^3/1+3x^2 Now, 1+g(x)/1 g(x) = 1+3x+x^3/1+3x^2/1 3x+x^3/1+3x^2 =1+3x^2+3x+x^3/1+3x^2 3x x^3 = (1+x)^3/(1 x)^3 Then, ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

If fx=log1+x/...

Question

If $f (x) = l o g (\frac{1 + x}{1 - x})$ and $g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$ , then f(g(x)) is equal to

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Solution

$3 f (x)$
$f (x) = l o g (\frac{1 + x}{1 - x})$ and $g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$
Now, $\frac{1 + g (x)}{1 - g (x)} = \frac{1 + \frac{3 x + x^{3}}{1 + 3 x^{2}}}{1 - \frac{3 x + x^{3}}{1 + 3 x^{2}}}$
$= \frac{1 + 3 x^{2} + 3 x + x^{3}}{1 + 3 x^{2} - 3 x - x^{3}} = \frac{(1 + x)^{3}}{(1 - x)^{3}}$
Then, $f (g (x)) = l o g (\frac{1 + g (x)}{1 - g (x)}) = l o g {(\frac{1 + x}{1 - x})}^{3}$
$= 3 l o g (\frac{1 + x}{1 - x}) = 3 f (x)$

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If f(x)=log(1+x1−x) and g(x)=3x+x31+3x2, then f(g(x)) is equal to

3f(x) f(x)=log(1+x1−x) and g(x)=3x+x31+3x2 Now, 1+g(x)1−g(x)=1+3x+x31+3x21−3x+x31+3x2 =1+3x2+3x+x31+3x2−3x−x3=(1+x)3(1−x)3 Then, f(g(x))=log(1+g(x)1−g(x))=log(1+x1−x)3 =3 log(1+x1−x)=3f(x)

If $f (x) = l o g (\frac{1 + x}{1 - x})$ and $g (x) = \frac{3 x + x^{3}}{1 + 3 x^{2}}$ , then f(g(x)) is equal to