Functions Question 174
Question: Let $ f(x)= \begin{cases} & \frac{x^{4}-5x^{2}+4}{|(x-1)(x-2)|},\ \ x\ne 1,\ 2 \\ & 6,,x=1 \\ & ,12,,x=2 \\ \end{cases} . $ Then $ f(x) $ is continuous on the set
Options:
A) R
B) $ R-{1} $
C) $ R-{2} $
D) $ f:R\to R $
Show Answer
Answer:
Correct Answer: D
Solution:
For any $ x\ne 1,2 $ we find that $ f(x) $ is the quotient of two polynomials and a polynomial is everywhere continuous. Therefore $ f(x) $ is continuous for all $ x\ne 1,2. $ Check continuity at $ x=1,2. $
BETA
