Question

If f(x) is defined in [a,b] where $ab\ge 0$, then the even extemsion of f(x) is

• A. f(-x), x $\epsilon$ [a,b]
• B. -f(-x), x $\epsilon$ [a,b]
• C. -f(-x), x $\epsilon$ [-b,-a]
• D. -f(-x), x $\epsilon$ [-b,-a]

Answer 1

The correct option is D

-f(-x), x $\epsilon$ [-b,-a]

To get even extension replace x by -x, i.e. f(x), here -x $\epsilon$ [a, b]

$\Rightarrow$ -x $\epsilon$ [ -b,-a] $\Rightarrow$ domain

[To understand how we get domain, we can consider the function, $\sqrt{x}$, $\sqrt{x}$ is defined for x > 0, whereas the even extension of $\sqrt{x}$, $\sqrt{-x}$ is defined when x < 0]