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

Question

2263 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-02T12:16:17

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

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

The function is a symmetry about $y$ $y$ axis

$f (x) = \sqrt{x^{2} - 3}$ $f(x) = sqrt (x^2-3)$

$f (- x) = \sqrt{{(- x)}^{2} - 3} = \sqrt{x^{2} - 3}$ $f(-x) = sqrt ((-x)^2-3) = sqrt (x^2-3)$

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

$y$ $y$ 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)=√x2−3f(x)= sqrt ( x^2 -3) is an even or odd function?