IB Mathematics Analysis and Approaches Question Type 4: Finding the Domain of More Complex Functions Exercises

Determine the domain of $f(x)=\sqrt{\frac{1}{x-1}}$.

Find the domain of $f(x)=\sqrt{\ln (x^2-4)}$.

Find the domain of $f(x)=\ln \left(\sqrt{x+2}\right)$.

Determine the domain of $f(x)=\ln (3x-6)$.

Find the domain of $f(x)=\sqrt{\ln \left(\frac{x+4}{2x-1}\right)}$.

Find the domain of the function $f(x)=(x-5{)}^{1/2}$.

Determine the domain of $f(x)=\ln (\ln (x))$.

Determine the domain of $f(x)=\ln (x-\sqrt{x-1})$.

Determine the domain of $f(x)=\sqrt{\ln (5-x)}$.

Find the domain of $f(x)=\sqrt{\ln \left(\sqrt{x-3}\right)}$.

Find the domain of $f(x)=\frac{1}{x^2-9}$.

Determine the domain of $f(x)=\ln \left(\frac{x-2}{x+3}\right)$.