[tex]g(x) = x^2 - 2 \text{ is even function }[/tex]
Solution:
Given that,
[tex]g(x) = x^2 - 2[/tex]
We have to find whether the above function is odd or even
If a function is: y = f(x)
If f(-x) = f(x), the function is even
If f(-x) = - f(x), the function is odd
Which is,
[tex]\mathrm{Even\:Function:\:\:A\:function\:is\:even\:if\:}f\left(-x\right)=f\left(x\right)\mathrm{\:for\:all\:}x\in \mathbb{R}\\\\\mathrm{Odd\:Function:\:\:A\:function\:is\:odd\:if\:}f\left(-x\right)=-f\left(x\right)\mathrm{\:for\:all\:}x\in \mathbb{R}[/tex]
From given,
[tex]g(x) = x^2 - 2[/tex]
Replace x with -x
[tex]g(-x) = (-x)^2 - 2\\\\g(-x) = x^2 - 2[/tex]
Therefore,
[tex]g(x) = g(-x)[/tex]
Thus the function g(x) is even
