Functions Question 586
Question: The range of the function $ f(x){{=}^{7-x}}{P_{x-3}} $ is
[AIEEE 2004]
Options:
A) {1, 2, 3, 4, 5}
B) (1, 2, 3, 4, 5, 6)
C) {1, 2, 3, 4}
D) {1, 2, 3}
Show Answer
Answer:
Correct Answer: D
Solution:
For $ ^{7-x}{P_{x-3}} $ to be defined, $ 7-x>0\Rightarrow x<7 $
$ x-3\ge 0\Rightarrow x\ge 3 $ ; $ 7-x\ge x-3\Rightarrow x\le 5 $
\ $ x\in { 3,,4,,5 } $
Þ $ f(3)=1,\ f(4)=3,f(5)=2 $
So, the range of function $ ={ 1,2,3 } $ .
BETA
