Functions
General
Grade 12
Question:
Let f : (-1,1) → ℝ be such that f(cos 40°) = \(\frac{2}{2 - \sec^2 \theta}\) for \(\theta \in \left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right)\). Then the value(s) of f(\(\frac{1}{3}\)) is (are) -
1 - \(\frac{\sqrt{3}}{2}\)
1 + \(\frac{\sqrt{3}}{2}\)
1 - \(\frac{\sqrt{2}}{3}\)
1 + \(\frac{\sqrt{2}}{3}\)
Step-by-Step Solution
Key Concept: General
(as we are getting two f images for one x in the domain)
Correct Answer: (zero marks to all)