Given the function f(x) with the following conditions:
We need to determine the value of \(f(f(f(a)))=21.\)
First, let's break it down step by step:
Now, we solve for a such that \(f(f(f(a)))=21.\)
Thus, the only solution that works is for a=12.
Now, let's compute the limit:
\(\lim_{x \to 12} f(x) = f(12) = 2 \times 12 = 24\)
So, the correct answer is 144.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: