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Find the domain of the composite function FOG

f(x)= 2/x-3; g(x)= 7/x

please show work so I can undestand

1 answer

(fog)(x) = f(g(x))

f(x) = 2/(x-3), so
f(g) = 2/(g-3), but
g(x) = 7/x, so
f(g(x)) = 2/(7/x - 3) = 2x/(7-3x)

the domain is all reals except where the denominator is zero. so, all reals except x = 7/3
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