Inverse Functions

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 inverse function of $y=x^3$ is ( ).
   • A．$y=\sqrt[3]{x}$
   • B．$y=3^x$
   • C．$y=x/3$
   • D．$y=x^3$
   Show answer & solution

   Answer: A

   Answer: A From $y=x^3$, interchange $x$ and $y$: $x=y^3$, hence $y=\sqrt[3]{x}$. Choose A.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math April 2026 Past Paper
   The inverse function of $y = 10 x + 3$ is
   • A．$y = \frac { x + 10 } { 3 }$
   • B．$y = \frac { x - 10 } { 3 }$
   • C．$y = \frac { x + 3 } { 10 }$
   • D．$y = \frac { x - 3 } { 10 }$
   Show answer & solution

   Answer: D

   Solve for $x : x = \frac { y - 3 } { 10 }$. Swap $x$ and $y : y = \frac { x - 3 } { 10 }$.
   Take the full CSCA Math April 2026 Past Paper — timed & graded
3. CSCA Math June 2026 Past Paper
   The inverse function of $y = 2x, x \in [-1, 1]$ is
   • A．$y = \frac{x}{2}, x \in [-1, 1]$
   • B．$y = \frac{x}{2}$
   • C．$y = \frac{x}{2}, x \in [-2, 2]$
   • D．$y = 2x, x \in [-1, 1]$
   Show answer & solution

   Answer: C

   Step 1, find the expression: from $y = 2x$ we get $x = \frac{y}{2}$; swapping $x$ and $y$ gives $y = \frac{x}{2}$. Step 2, determine the domain: the range of the original function is the domain of the inverse. For $x \in [-1, 1]$, $y = 2x \in [-2, 2]$, so the inverse is $y = \frac{x}{2}, x \in [-2, 2]$. Choose (C).
   Take the full CSCA Math June 2026 Past Paper — timed & graded