Functions Question 559
Question: Let $ f:R\to R $ be a function such that $ f(x)=ax+3sinx+4cosx. $ Then f(x) is invertible if
Options:
A) $ a\in (-5,5) $
B) $ a\in (-\infty ,-5) $
C) $ a\in (0,+\infty ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f’(x)=a+3\cos x+4\sin x $ $ f(x) $ is one-one if $ f’(x)>0 $ for all x or $ f’(x)<0 $ for all x. So, $ f’(x)<0\forall x, $ if $ a<-5 $ and $ f’(x)>0\forall x, $ if $ a>5 $
$ \therefore ,a\in (-\infty ,-5)\cup (5,\infty ) $
BETA
