IB Mathematics Applications & Interpretation Question Type 4: Finding the Domain of More Complex Functions Exercises

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

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

Find the domain of the function $f(x)=\sqrt{\ln (x^2+2x+1)}$.

Determine the domain of $p(x)=\ln (5-\sqrt{x+4})$.

Find the domain of $h(x)=\sqrt{\frac{x-3}{x-1}}$.

Determine the domain of $t(x)=\ln (\sqrt{x-3}-1)$.

Find the domain of $s(x)=\frac{1}{\sqrt{1-e^{-x}}}$.

Determine the domain of $y(x)=\ln (1-\frac{1}{x-2})$.

Determine the domain of $r(x)=\sqrt{\ln (2x-5)+1}$.

Determine the domain of $v(x)=\ln (\ln (x^2-1))$.

Find the domain of $u(x)=\sqrt{\frac{\ln x}{x-1}}$.

Find the domain of $w(x)=\sqrt{\frac{x+2}{\ln (x+3)}}$.