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 $p(x)=\ln\bigl(5-\sqrt{x+4}\bigr)$.

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

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

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

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

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

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

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

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