Form 4 Additional Mathematics Bab 1: Functions
Instructions
Answer all SPM-level questions based on Chapter 1: Functions. Show clear algebraic workings where required.
10 questions · 25 marks total
1. Given f: x ↦ |2x - 5|, calculate the images of x = -1 and x = 4.
Short Answer · 2m2. Fill in the blank: A relation is classified as a function if and only if each object in the domain has __________ image in the codomain.
Fill in the Blank · 1m3. True or False: If f(x) is a quadratic function defined for all real numbers x, its inverse function f⁻¹(x) exists for all real numbers.
True / False · 1m4. Given the function h(x) = 2x + 53x - 6, state the condition for x such that h(x) is defined.
Short Answer · 2m5. Given function f: x ↦ px + qx - 2, x ≠ 2. If f(3) = 7 and f⁻¹(1) = 5, find the values of p and q.
Short Answer · 4m6. A function is defined as f(x) = 4x - 3. Find the value of x such that f(x) = f⁻¹(5).
Short Answer · 3m7. Given that g(x) = x + 3 and composite function fg(x) = x² + 6x + 5, determine the function f(x).
Short Answer · 3m8. Given the functions f(x) = 2x + k and g(x) = 3x - 2. If fg(x) = gf(x) for all values of x, find the value of the constant k.
Short Answer · 3m9. True or False: The graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.
True / False · 1m10. The domain of f(x) = |x - 2| - 1 is -1 ≤ x ≤ 5. (a) Sketch the graph of f(x). (b) State the corresponding range of f(x). (c) Determine whether f⁻¹ exists over this domain, giving a reason.
Short Answer · 5m