Functions: domain, range, inverse and graphs sheetStructured-answer frameGiven f(x) = 4x − 8: (a) find f(3); (b) state the domain and range; (c) find f⁻¹(x) and check your answer.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Evaluate. f(3) = 4(3) − 8 = 4.
- 2 · Domain and range. A linear function accepts any real x and gives any real y: both are all real numbers.
- 3 · Swap x and y. y = 4x − 8 becomes x = 4y − 8.
- 4 · Solve for y. 4y = x + 8, so f⁻¹(x) = (x + 8)/4.
- 5 · Check. f(f⁻¹(x)) = 4 × (x + 8)/4 − 8 = x. ✓ Also f(3) = 4 and f⁻¹(4) = 12/4 = 3. ✓
