If f(x)=4x+36x−4,x≠23,and(f0f)(x)=g(x), (x)where g:R−{23}→R−{23}, then (gog) (4) is equal to

g(x)=f(4x−36x−4)=4(4x−36x−4)−36(4x−36x−4)−4=16x−12−18x+1224x−18−24x+16=−2x−2=xgog(4)=g(g(4))=g(4)=4

If f(x)=4x+36x−4,x≠23,and(f0f)(x)=g(x), (x)where g:R−{23}→R−{23}, then (gog) (4) is equal to

g(x)=f(4x−36x−4)=4(4x−36x−4)−36(4x−36x−4)−4=16x−12−18x+1224x−18−24x+16=−2x−2=xgog(4)=g(g(4))=g(4)=4

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If $f (x) = \frac{4 x + 3}{6 x - 4}, x \neq \frac{2}{3}, a n d (f 0 f) (x) = g (x),$ (x)where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}},$ then (gog) (4) is equal to

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-4

$\frac{19}{20}$

$- \frac{19}{20}$

answer is A.

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$g (x) = f (\frac{4 x - 3}{6 x - 4}) = \frac{4 (\frac{4 x - 3}{6 x - 4}) - 3}{6 (\frac{4 x - 3}{6 x - 4}) - 4} = \frac{16 x - 12 - 18 x + 12}{24 x - 18 - 24 x + 16} = \frac{- 2 x}{- 2} = x$

$g o g (4) = g (g (4)) = g (4) = 4$

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If f(x)=4x+36x−4,x≠23,and(f0f)(x)=g(x), (x)where g:R−{23}→R−{23}, then (gog) (4) is equal to

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If $f (x) = \frac{4 x + 3}{6 x - 4}, x \neq \frac{2}{3}, a n d (f 0 f) (x) = g (x),$ (x)where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}},$ then (gog) (4) is equal to