Grade 12 Maths · Functions · Paper 1

Inverse Graphs Grade 12

Real Inverse Graphs past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 32 past paper questions
skills: 7 skills
videos: 7 videos

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Question 6.3 · May/June 2025 · Paper 1 · National (DBE) · 4 marks

The graphs of

f (x) = p^{x} + q

and

g (x) = m x + c

are drawn below.

A (3; 4)

is the point of intersection of

f

and

g

B (0; - 3)

is the y-intercept of

f

. E is the x-intercept of

g

6.3 The graph of

g^{- 1}

, the inverse of

g

, also passes through B. Determine the equation of

g

in the form

y = \dots

(4)

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

Inverse Graphs skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Inverse Graphs Grade 12 questions and answers

Try each one on paper before you open the memo.

4. 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
5. Question 5.1 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
In the diagram, the graphs of $f (x) = lo g_{a} x$ and $g$ are drawn. Graph $g$ is the reflection of $f$ in the line $y = x$ . Graph $f$ passes through the point P $(4; 2)$ . Q is the $x$ -intercept of $f$ and R is the $y$ -intercept of $g$ .
5.1 Write down the coordinates of P $^{'}$ , the image of P on $g$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  x-coordinate identification2
  1 mark · Find the equation of an inverse
2. ✓
  y-coordinate identification4
  1 mark · Find the equation of an inverse
6. 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
7. Question 4.2 · March 2025 · Provincial · 3 marks
The diagram below shows the graph of $k (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $k$ .
4.2 Draw the graph of $h$ , the reflection of $k$ in the line $y = x$ , showing all the intercepts with the axes and the coordinates of another point on the graph.(3)
Show the memo (3 ticks)Memo
1. ✓
  Draw shapeCorrect shape (logarithmic function shape)
  1 mark · Sketch an inverse graph
2. ✓
  Indicate x-interceptx-intercept at $(1; 0)$
  1 mark · Find the x-intercepts
3. ✓
  Indicate another pointPoint $(3 \frac{3}{8}; 3)$
  1 mark · Find the equation of an inverse
8. 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
9. Question 3.4 · March 2024 · Paper 1 · Provincial · 2 marks
The diagram shows the graph of $f (x) = \frac{3}{x + 2} + 1$
3.4 The graph of $g$ is formed by first reflecting $f$ in the $y$ -axis and then translating it upwards by 2 units. Determine the equation of $g$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply transformations to function $f$ Reflection in $y$ -axis: $f (- x) = \frac{3}{- x + 2} + 1$
  Translate 2 units up: $g (x) = \frac{3}{- x + 2} + 1 + 2$
  $g (x) = \frac{3}{- x + 2} + 3$
  1 mark · Shift or reflect a graph
2. ✓
  Simplify final equation $g (x) = \frac{- 3}{x - 2} + 3$
  1 mark · Shift or reflect a graph
10. 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)
Show the memo (3 ticks)Memo
1. ✓
  Swap variables $y = 3 x^{2} ⟹ x = 3 y^{2}$
  1 mark · Find the equation of an inverse
2. ✓
  Isolate $y$ $y^{2} = \frac{1}{3} x$
  $y = \pm \frac{1}{3} x$
  1 mark · Find the equation of an inverse
3. ✓
  Write restricted domain equation $y = \frac{1}{3} x$ for $x \geq 0$
  1 mark · Restrict domain for an inverse

Inverse Graphs Grade 12 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

1) Vertical line test gr 12Kevinmathscience

Reflections of the Exponential GraphMaths101 with Jana van Niekerk

Exponential Domain Range| Grade 11 FunctionsKevinmathscience

Writing Logarithmic Equations In Exponential FormThe Organic Chemistry Tutor

8) Inverse equations | Many examplesKevinmathscience

3) Inverse of parabola | Part 1Kevinmathscience

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