Answer:
4.[tex]f(x)=|x|[/tex]
Step-by-step explanation:
We know that
If f(x)=f(-x)
Then, the function is called even function.
1.[tex]f(x)=x^{4-x^2}[/tex]
[tex]f(-x)=(-x)^{4-x^2}[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, the function is not even.
2.[tex]f(x)=x^2-3x+2[/tex]
[tex]f(-x)=x^2+3x+2[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, the function is not even.
3.[tex]f(x)=\sqrt{x-2}[/tex]
[tex]f(-x)=\sqrt{-x-2}[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, the function is not even.
4.[tex]f(x)=|x|[/tex]
[tex]f(-x)=|-x|=|x|=f(x)[/tex]
Therefore, the function is even.
Option (4) is true.
