Prove the following

Question:

If $p(x)=x+3$, then $p(x)+p(-x)$ is equal to

(a) 3

(b) $2 x$

(c) 0

(d) 6

Solution:

(d) Given $p(x)=x+3$, put $x=-x$ in the given equation, we get $p(-x)=-x+3$

Now, $p(x)+p(-x)=x+3+(-x)+3=6$

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