Question

Let $f\left(x\right)$ be an even function in $R$. If $f\left(x\right)$ is monotonic increasing in $[2,6]$ then

• A. $f\left(3\right)>f(-5)$
• B. $f(-2)<f\left(2\right)$
• C. $f(-2)>f\left(2\right)$
• D. $f(-3)<f\left(5\right)$

Answer 1

The correct option is D $f(-3)<f\left(5\right)$

Since, the function is even function, we have $f\left(x\right)=f\left(-x\right)$.
and the function is monotonic increasing in $\left[2,6\right]$, we have $f\left(x\right)\le f\left(y\right)$, whenever $x\le y$.
Combining the two we get, $f\left(-x\right)=f\left(x\right)\le f\left(y\right)$ if and $2\le x\le y\le 6$.
option D satisfies the criterion, hence the correct answer is option D.