Question

If $p\left( x \right)=x+3$ , then $p\left( x \right)+p\left( -x \right)$ is equal to:
A. 3
B. 2x
C. 0
D. 6

Answer 1

Hint: Here, we are asked to find the value of $p\left( x \right)+p\left( -x \right)$. To solve this first we need to find $p\left( -x \right)$ by substituting ‘-x’ in $p\left( x \right)$ . Then we will add $p\left( x \right)$ and $p\left( -x \right)$ to find the answer.

Complete step-by-step answer:
In this question it is given that, $p\left( x \right)=x+3$ .
Here, we need to find $p\left( x \right)+p\left( -x \right)$ .
To find this first we will find \[p\left( -x \right)\]
Let us take $p\left( x \right)=x+3$…………………… (1)
 To find \[p\left( -x \right)\] we will put the –x in the place of x in equation (1).
So, we get
$\Rightarrow p\left( -x \right)=\left( -x \right)+3$
$\therefore p\left( -x \right)=-x+3$………………………….(2)
Now, we will find the value of $p\left( x \right)+p\left( -x \right)$ by taking the values from equation (1) and (2).
$\begin{align}
  & p\left( x \right)+p\left( -x \right)=\left( x+3 \right)+\left( -x+3 \right) \\
 & =x+3-x+3 \\
\end{align}$
By cancelling x and –x we will get –
$\begin{align}
  & =3+3 \\
 & =6 \\
\end{align}$
$\therefore p\left( x \right)+p\left( -x \right)=6$
Hence, option (D) is the correct answer.


Note: While solving this question students should be very careful as they may do mistake while finding $p\left( -x \right)$ by taking $p\left( -x \right)=-\left( x+3 \right)=-x-3$ which is wrong and this may leads to get wrong answer.