Functions Question 696
Question: The domain of the function $ f(x){{=}^{24-x}}{C_{3x-1}}{{+}^{40-6x}}{C_{8x-10}} $ is,
Options:
A) $ {2,3} $
B) $ {1,2,3} $
C) $ {1,2,3,4} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ ^{24-x}{C_{3x-1}} $ is defined if, $ 24-x>0,3x-1\ge 0 $ And $ 24-x\ge 3x-1 $
$ \Rightarrow x<24,x\ge \frac{1}{3} $ And $ x\le \frac{25}{4}\Rightarrow \frac{1}{3}\le x\le \frac{25}{4} $ $ ^{40-6x}{C_{8x-10}} $ is defined if $ 40-6x>0,8x-10\ge 0 $ And $ 40-6x\ge 8x-10 $
$ \Rightarrow x<\frac{20}{3},x\ge \frac{5}{4}andx\le \frac{25}{7} $
$ \Rightarrow \frac{5}{4}\le x\le \frac{25}{7} $ From (1) and (2), we get $ \frac{5}{4}\le x\le \frac{25}{7} $ But $ 24-x\in N,\therefore x $ must be an integer, $ x=2,3. $ Hence domain $ (f)={2,3}. $
BETA
