which of the following is an even function?\n$f(x) = |x|$\n$f(x) = x^3 - 1$\n$f(x) = -3x$\n$f(x) = \\sqrt3{x}$

Explanation:

Step1: Recall even function rule

A function $f(x)$ is even if $f(-x) = f(x)$ for all $x$ in its domain.

Step2: Test $f(x)=|x|$

$f(-x) = |-x| = |x| = f(x)$. This satisfies the even function condition.

Step3: Test $f(x)=x^3-1$

$f(-x) = (-x)^3 -1 = -x^3 -1$, which is not equal to $x^3-1$. Not even.

Step4: Test $f(x)=-3x$

$f(-x) = -3(-x) = 3x = -f(x)$, this is an odd function, not even.

Step5: Test $f(x)=\sqrt[3]{x}$

$f(-x) = \sqrt[3]{-x} = -\sqrt[3]{x} = -f(x)$, this is an odd function, not even.

Answer:

A. $f(x) = |x|$