How do you know if $f(x)= sqrt ( x^2 -3)$ is an even or odd function?

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Answer 1 · 2018-07-02T12:16:17

$f(x)$ is an "even" function.

A function is "even" when $f(-x)= f(x)$ for all $x$

The function is a symmetry about $y$ axis

$f(x) = sqrt (x^2-3)$

$f(-x) = sqrt ((-x)^2-3) = sqrt (x^2-3)$

$f(-x)= f(x)$ , the graph also shows its symmetry about

$y$ axis , so it is an "even" function.

graph{(x^2-3)^0.5 [-20, 20, -10, 10]} [Ans]

How do you know if f(x)= sqrt ( x^2 -3)f(x)= sqrt ( x^2 -3) is an even or odd function?