Inverse Functions (Grade 12) — Worksheet & Memo

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Grade 12 · Functions

Inverse Functions (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Determine the equation of h⁻¹, the inverse of h(x) = 3x − 6, in the form y = …
(2)
x = 3y − 6 → y = 13x + 2✓✓ (2)
2
Determine the inverse of f(x) = 2x².
(2)
x = 2y² → y = ±x2✓✓ (2)
3
Is the inverse of f(x) = 2x² a function? Give a reason.
(2)
No — because of the ±, one x-value gives two y-values, so it fails the vertical line test.✓✓ (2)
4
Restrict the domain of f(x) = 2x² so that f⁻¹ is a function.
(2)
x ≥ 0 (or x ≤ 0)✓✓ (2)
5
Determine the equation of k⁻¹ if k(x) = 2^x.
(2)
y = log₂ x✓✓ (2)
6
Write down the domain and range of k⁻¹ if k(x) = 2^x.
(2)
Domain x > 0; range y ∈ ℝ✓✓ (2)
7
The graph of f⁻¹ is the reflection of f in which line?
(2)
y = x✓✓ (2)
8
The point (2 ; 7) lies on f. Write down a point on f⁻¹.
(2)
(7 ; 2)✓✓ (2)

TOTAL: 16 marks