Functions Question 652
Question: Range of $ f(x)=\frac{x^{2}+34x-71}{x^{2}+2x-7} $ is
[Roorkee 1983]
Options:
A) [5, 9]
B) $ (-\infty ,\ 5]\cup [9,\ \infty ) $
C) (5, 9)
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ \frac{x^{2}+34x-71}{x^{2}+2x-7}=y $
$ \Rightarrow x^{2}(1-y)+2,(17-y),x+(7y-71)=0 $ For real value of $ x,B^{2}-4AC\ge 0 $
$ \Rightarrow y^{2}-14y+45\ge 0\Rightarrow y\ge 9,y\le 5 $ .
BETA
