which of the following is an even function?\no (f(x)=|x|)\no (f(x)=x^{3}-1)\no (f(x)= - 3x)\no (f(x)=sqrt3{x})

Explanation:

Step1: Recall even - function definition

An even function satisfies (f(x)=f( - x)) for all (x) in the domain of (f).

Step2: Check (f(x)=|x|)

If (f(x)=|x|), then (f(-x)=|-x| = |x|). Since (f(x)=f(-x)), (y = |x|) is an even function.

Step3: Check (f(x)=x^{3}-1)

(f(-x)=(-x)^{3}-1=-x^{3}-1). Since (f(-x)\neq f(x)) (because (-x^{3}-1\neq x^{3}-1)), (y = x^{3}-1) is not an even function.

Step4: Check (f(x)=-3x)

(f(-x)=-3(-x)=3x). Since (f(-x)\neq f(x)) (because (3x\neq - 3x)), (y=-3x) is not an even function.

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

(f(-x)=\sqrt[3]{-x}=-\sqrt[3]{x}). Since (f(-x)\neq f(x)) (because (-\sqrt[3]{x}\neq\sqrt[3]{x})), (y = \sqrt[3]{x}) is not an even function.

Answer:

(f(x)=|x|)