Question

find the domain of the composite function fog
f(x)=2/x-3; g(x)=7/x

Answer 1

since you cannot divide by zero, the domain of \(g\) is all numbers except 0
so 0 is not in the domain of \(f\circ g\)
also we have to make sure that the denominator of \(f\) is not zero as well, so \(\frac{7}{x}\neq 3\)
meaning \(x\neq \frac{7}{3}\)
finally lets compute
\[f\circ g(x)=f(g(x))=f(\frac{x}{7})=\frac{2}{\frac{7}{x}-3}\]
\[=\frac{2x}{7-3x}\]

Answer 2

sorry typo in second to last line. should be
\[f\circ g(x)=f(g(x))=f(\frac{7}{x})=\frac{2}{\frac{7}{x}-3}\]