Question

Let $f:R\to R$ is a function satisfying $f(2-x)=f(2+x)$ and $f(20-x)=f\left(x\right),\forall x\in R$. For this function $f$ answer the following question.Graph of $y=f\left(x\right)$ is

• A. symmetrical about $x=16$
• B. symmetrical about $x=5$
• C. symmetrical about $x=8$
• D. symmetrical about $x=20$

Answer 1

The correct option is A symmetrical about $x=16$

$f(2-x)=f(2+x)$

Replace $x\to x+2$

$f(-x)=f(x+4)..............................................1$
$f(20-x)=f\left(x\right)$

Replace $x\to -x$
$f(20+x)=f(-x)...........................................2$

Now, $f(20+x)=f(4+x)$

Replace $x$ by $x-4$

From 1 and 2
$f(20+x-x)=f(4+x-x)$

$f(x+16)=f\left(x\right)$

So, $y$ is symmetrical about $x=16$