If $f(x)$ is an even function passing through $(2,5)$ then what other point must it pass through?

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Answer 1 · 2017-12-21T18:21:21

If $f(x)$ is an even function including the point $(2, 5)$ then it will also include the point $(-2, 5)$ ...

To say that $f(x)$ is an even function is to say that for any $x$ in its domain $f(-x) = f(x)$ .
To say that $(2, 5)$ is a point on the graph of $f(x)$ is to say that $f(2) = 5$ .

Hence we can deduce that $f(-2) = 5$ and $(-2, 5)$ is also a point on the graph of $f(x)$ .

If f(x)f(x) is an even function passing through (2,5)(2,5) then what other point must it pass through?