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Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in ...

Let `g(x)=f(x)-1.` If `f(x)+f(1-x)=2AAx in R ,` then `g(x)` is symmetrical about. (a)The origin (b) the line`x=1/2` (c) the point (1,0) (d) the point `(1/2,0)`

A

the orgin

B

the line`x=(1)/(2)`

C

the point (1, 0)

D

the point `((1)/(2),0)`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)-1+f(1-x)-1=0`
So, `g(x)+g(1-x)=0.`
Replacing x by `x+(1)/(2), " we get " g((1)/(2)+x)+g((1)/(2)-x)=0.`
So, it is symmetrical about `((1)/(2), 0)`.
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