Question

Let $f\left(x\right)=\{\begin{array}{cc}4,& x<-1\\ -4x& -1\le x\le 0\end{array}$
If $f\left(x\right)$ is an even function in R then the definition of $f\left(x\right)$ in $(0,\infty )$ is

• A. $f\left(x\right)=\{\begin{array}{c}4x,0<x\le 1\\ 4,x>1\end{array}$
• B. $f\left(x\right)=\{\begin{array}{c}4x,0<x\le 1\\ -4,x>1\end{array}$
• C. $f\left(x\right)=\{\begin{array}{c}4,0<x\le 1\\ 4x,x>1\end{array}$
• D. None of these

Answer 1

The correct option is A $f\left(x\right)=\{\begin{array}{c}4x,0<x\le 1\\ 4,x>1\end{array}$

Given, $f\left(x\right)=\{\begin{array}{c}4,x<-1\\ -4x,-1\le x\le 0\end{array}$

Also given that $f\left(x\right)$ is even function in R

$\therefore f(-x)=f\left(x\right)=\{\begin{array}{c}4,-x<-1\\ -4(-x),-1\le -x\le 0\end{array}$

or $f\left(x\right)=\{\begin{array}{c}4,x>1\\ 4x,0\le x\le 1\end{array}$