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

Answer 1

Answer: (A)

$f\left(x\right)=\{\begin{array}{cc}4x& 0<x\le 1\\ 4& x>1\end{array}$

$f\left(x\right)$ is even over $R$ mean, $f\left(x\right)=f(-x)$

Therefore

$f\left(x\right)=4$ for $x>1$

and $f\left(x\right)=-4x$ for $xϵ(0,1]$

$\therefore f\left(x\right)=\{\begin{array}{cc}4x& 0<x\le 1\\ 4& x>1\end{array}$