Question

Find the domain:

\[f(x)=\frac{ 1 }{ \frac{ 4 }{ x-1 } -2}\]

Answer 1

Well, you don't want 4/(x-1) to equal infinity or 2, so solve for x in those values.

Answer 2

\(\bf f(x)=\cfrac{ 1 }{ \frac{ 4 }{ x-1 } -2}
\\ \quad \\
f(x)=\cfrac{ 1 }{ \frac{ 4 }{ {\color{brown}{ +1}}-1 } -2}\to \cfrac{ 1 }{ \frac{ 4 }{ {\color{brown}{ 0}} } -2}\quad {\color{brown}{ undefined}}
\\ \quad \\
or
\\ \quad \\
f(x)=\cfrac{ 1 }{ {\color{brown}{ +2}} -2}\to \cfrac{ 1 }{ {\color{brown}{ 0}} }\quad {\color{brown}{ undefined}}\)

Answer 3

thank you both