Answer:
f(x) = |x|
Step-by-step explanation:
A function f(x) is called even function,
If f(-x) = f(x),
In first option
![f(x)=|x|](https://tex.z-dn.net/?f=f%28x%29%3D%7Cx%7C)
Since, f(-x) = |-x| = |x| = f(x)
⇒ f(x) is an even function,
In second option,
![f(x)=x^3-1](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3-1)
![f(-x)=(-x)^3-1 = -x^3 - 1\neq f(x)](https://tex.z-dn.net/?f=f%28-x%29%3D%28-x%29%5E3-1%20%3D%20-x%5E3%20-%201%5Cneq%20f%28x%29)
⇒ f(x) is not an even function,
In third option,
![f(x)=-3x](https://tex.z-dn.net/?f=f%28x%29%3D-3x)
![f(-x)=-3(-x)=3x\neq f(x)](https://tex.z-dn.net/?f=f%28-x%29%3D-3%28-x%29%3D3x%5Cneq%20f%28x%29)
⇒ f(x) is not an even function.