Answer
False.
Work Step by Step
To find $f(-x)$, replace $x$ with $-x$ in $f(x)$ to get $$f(-x)=(-x)^2+2(-x)+7=x^2-2x+7$$ However, $x^2-2x+7 = f(-x) \ne f(x)$. Therefore, the statement is false.
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