Functions Question 296
Question: If the function $ f(x)=, \begin{cases} 5x-4 & , & if & 0<x\le 1 \\ 4x^{2}+3bx & , & if & 1<x<2 \\ \end{cases} . $ is continuous at every point of its domain, then the value of b is
[RPET 2000]
Options:
A) ? 1
B) 0
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x) $ is continuous at every point of its domain,
Þ $ \underset{x\to {1^{-}}}{\mathop{\lim }},f(x)=\underset{x\to {1^{+}}}{\mathop{\lim }},f(x)=f(1) $
Þ $ 5\times 1-4=4\times 1+3\times b\times 1 $
Þ $ 1=4+3b $
Þ $ 3b=-3 $
Þ $ b=-1 $ .
BETA
