Question

If f(x)= the square root of 2-x and g(x) is 3/(x-1), find the domains of: D f of g

Answer 1

\[f(x)=\sqrt{2-x}\]
\[g(x)=\frac{3}{x-1}\] domain of \(f\) is found by solving \(2-x\geq 0\) for \(x\)
domain of \(g\) is found by solving \(x-1\neq 0\)

Answer 2

\[f(g(x))=f(\frac{3}{x-1})=\sqrt{2-\frac{3}{x-1}}\] then some algebra