Statement-1: The domain of definition of the function `f(x)=e^(2x)+cos^(-1)((x)/(2)-1)` , is `(0,1) cup (1,2) cup (2,3) cup (3,4)` Statement:- The domain of ` cos^(-1)""((x)/(2)-1) is [0,4]`.

Options

A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.

Answer

D

Explanation

Clearly , ` cos^(-1)""((x)/(2)-1)` is defined for all x satisfying
`-1 le ((x)/(2)-1) le1 ` i.e., ` o le (x)/(2) or x in [0,4]`
So, Statement-2 is not true.
The domain of definition of ` e^(2x), cos^(-1)((x)/(2)-1)` and ` log sqrt({x})` are `R cap [0,4] cap R-Z=(0,1) cup (,2) cup (2,3) cup (3,4)`
So, statement-1 is true.