Function Domains

How the real exam tests it

Questions from real CSCA papers that test this concept. Work each one out before you open the answer.

1. CSCA Math December 2025 Past Paper
   The domain of $y=\frac{1}{\sqrt{x+1}}$ is ( ).
   • A．$(0,+\infty)$
   • B．$[-1,+\infty)$
   • C．$(-1,+\infty)$
   • D．$(-\infty,-1)$
   Show answer & solution

   Answer: C

   Answer: C The denominator cannot be zero and the radicand must be positive, so $x+1>0$. Choose C.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math April 2026 Past Paper
   The domain of $f ( x ) = \sqrt { 3 x }$ is
   • A．$( 0 , + \infty )$
   • B．$( - \infty , + \infty )$
   • C．$[ 1 , + \infty )$
   • D．$[ 0 , + \infty )$
   Show answer & solution

   Answer: D

   The radicand must be non-negative: $3 x \geq 0 \Rightarrow x \geq 0$. Domain: $[ 0 , + \infty )$.
   Take the full CSCA Math April 2026 Past Paper — timed & graded
3. CSCA Math June 2026 Past Paper
   The domain of the function $y = \frac{1}{x-1} + \frac{1}{x-2} + \frac{1}{x-3}$ is
   • A．$(-\infty, 1) \cup (1, 2) \cup (2, 3) \cup (3, +\infty)$
   • B．$\{ 1, 2, 3 \}$
   • C．$[1, 3]$
   • D．$\mathbb{R}$
   Show answer & solution

   Answer: A

   None of the three denominators may be zero: $x \neq 1$, $x \neq 2$, $x \neq 3$. Removing these three points from the number line, the domain is $(-\infty, 1) \cup (1, 2) \cup (2, 3) \cup (3, +\infty)$. Choose (A).
   Take the full CSCA Math June 2026 Past Paper — timed & graded