Domains of functions¶
Exercises · Functions · with worked solutions · PDF
Exercise 1
Determine the domain of the function:
\[
f(x) = \frac{\log_2 (3+x)}{\sqrt[3]{x+2}}
\]
it is determined by studying the numerator and the denominator of the function
-
The numerator:
The function \(\log_2 t\) is defined for \(t > 0\), hence the function \(\log_2 (3+x)\) is defined for \(3+x > 0\), i.e., \(x > -3\).
-
The denominator:
The function \(\sqrt[3]{t}\) is always defined; however, since it is in the denominator, it must not vanish. Hence we impose \(\sqrt[3]{x+2} \neq 0\), i.e., \(x \neq -2\).
Hence the domain is
\[
(-3,-2) \cup (-2,+\infty)
\]
Exercise 2
Determine the domain of the function:
\[
f(x)=\sqrt{2^x-8} \cdot \log |x-4|
\]
Exercise 3
Determine the domain of the function:
\[
f(x)=\tan(\log x)
\]
Exercise 4
Determine the domain of the function:
\[
f(x)=\log(\tan x)
\]