Sets Relations And Functions Question 4
Question: Let $ g(x)=f(x)-1. $ If $ f(x)+f(1-x)=2\forall x\in R $ , then $ g(x) $ is symmetrical about
Options:
A) the origin
B) the line $ x=\frac{1}{2} $
C) the point (1, 0)
D) the point $ ( \frac{1}{2},0 ) $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ f(x)-1+f(1-x)-1=0 $ So, $ g(x)+g(1-x)=0. $
Replacing x by $ x+\frac{1}{2} $ , we get $ g( \frac{1}{2}+x )+g( \frac{1}{2}-x )=0. $
So, it is symmetrical about $ ( \frac{1}{2},0 ) $
BETA
