Grade 12 Maths · Functions

Restrict domain for an inverse

Limit the x-values of a parabola, like x ≥ 0, so that its inverse is a function (for example y = x², x ≥ 0 has inverse y = √x).

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3) Inverse of parabola | Part 1Kevinmathscience

3) Inverse of parabola | Part 2Kevinmathscience

How to Restrict the Domain so the Inverse is a FunctionMario's Math Tutoring

Inverse Functions (4 of 4: Restriction the Domain to get an Inverse Function of Even Functions)Eddie Woo

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Question 5.1 · March 2024 · Paper 1 · Provincial · 3 marks

Given:

f (x) = 3 x^{2}

where

x \geq 0

5.1 Determine the equation of

f^{- 1}

.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: restrict domain for an inverse

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3. Question 8.3.3 · November 2024 · Paper 1 · National (DBE) · 3 marks
8.3 Given: $f (x) = - 6 x^{2}$
8.3.3 Determine the equation of $f^{- 1}$ for $f^{- 1} (x) \leq 0$ . Write your answer in the form $y = ...$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Swap x and y $x = - 6 y^{2}$
  1 mark · Find the equation of an inverse
2. ✓
  Solve for y $y^{2} = - \frac{x}{6}$
  $y = \pm - \frac{x}{6}$
  1 mark · Find the equation of an inverse
3. ✓
  Apply restrictionSince $y \leq 0$ :
  $y = - - \frac{x}{6}$
  1 mark · Restrict domain for an inverse
4. Question 3.2.3 · March 2025 · Provincial · 3 marks
Given: $f (x) = (x - 1)^{2} - 9$
3.2 Consider the function $g (x) = x^{2}$ .
3.2.3 Determine the inverse of $g$ in the form $y = ...$ (include all restrictions).(3)
Show the memo (3 ticks)Memo
1. ✓
  Interchange x and y $x = y^{2}$
  1 mark · Find the equation of an inverse
2. ✓
  Solve for y $y = \pm x$
  1 mark · Find the equation of an inverse
3. ✓
  State restriction $x \geq 0$
  1 mark · Restrict domain for an inverse
5. Question 4.1.1 · March 2025 · Provincial · 3 marks
4.1 The graph of $f^{- 1} (x) = 3 x$ , $x \geq 0$ is drawn. $f^{- 1}$ passes through A(3; 3).
4.1.1 Determine the equation of $f$ in the form $y = ...$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Swap x and y in inverse equation $x = 3 y$
  1 mark · Find the equation of an inverse
2. ✓
  Solve for y $x^{2} = 3 y \to y = \frac{x ^{2}}{3}$
  1 mark · Find the equation of an inverse
3. ✓
  Include domain restriction $x \geq 0$
  1 mark · Restrict domain for an inverse

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