Functions Question 722
Question: If $ f(x)=\frac{\sin ([x]\pi )}{x^{2}+x+1} $ where [.] denotes the greatest integer function, then
Options:
A) f is one-one
B) f is not one-one and non-constant
C) f is a constant function
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x)=\frac{\sin [x]\pi }{x^{2}+x+1} $ Let $ [x]=n\in $ integer
$ \therefore \sin [x]\pi =0 $ Or $ f(x)=0 $ Hence, f(x) is constant function.
BETA
