Question

Let $n$ be the natural number. Then the range of the function $ f(n){{=}^{8-n}}{{p}_{n-4}},4\le n\le 6, $ is

• A. $\{1, 2, 3, 4\}$
• B. $\{1, 2, 3, 4, 5, 6\}$
• C. $\{1, 2, 3\}$
• D. $\{1, 2, 3, 4, 5\}$
• E. $ \phi $

Answer 1

Answer: (C)

Given that, $ y=2{{e}^{2x}}-{{e}^{-x}} $
On differentiating w.r.t. $ x, $ we get $ {{y}_{1}}=4{{e}^{2x}}+{{e}^{-x}} $
Now, on again differentiating w.r.t. $ x, $
we get $ {{y}_{2}}=8{{e}^{2x}}-{{e}^{-x}} $ Now, $ {{y}_{2}}-{{y}_{1}}-2y $
$=8{{e}^{2x}}-{{e}^{-x}}-4{{e}^{2x}}-{{e}^{-x}}-4{{e}^{2x}}+2{{e}^{-x}} $
$=0 $