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which functions are even? check all of the boxes that apply. f (x) = x superscript 4 baseline minus x squared f (x) = x squared minus 3 x + 2 f (x) =

Sagot :

Function (D) f(x) = |x| is even.

What are functions?

  • A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
  • Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

To find which functions are even:

We are aware that a function is even when f(x) = f(-x).

(A)

[tex]$\begin{aligned}&\text f(x)=x^{4-x^2} \\&f(-x)=(-x)^{4-x^2} \\&f(x) \neq f(-x)\end{aligned}$[/tex]

So, the function is not even.

(B)

[tex]$\begin{aligned}& f(x)=x^2-3 x+2 \\&f(-x)=x^2+3 x+2 \\&f(x) \neq f(-x)\end{aligned}$[/tex]

So, the function is not even.

(C)

[tex]$\begin{aligned}&\text f(x)=\sqrt{x-2} \\&f(-x)=\sqrt{-x-2} \\&f(x) \neq f(-x)\end{aligned}$[/tex]

So, the function is not even.

(D)

[tex]f(x)=|x|\\f(-x)=|-x|=|x|=f(x)[/tex]

So, the function is even.

Therefore, function (D) f(x) = |x| is even.

Know more about functions here:

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The complete question is given below:

Which functions are even? Check all of the boxes that apply.

a. F (x) = x Superscript 4 Baseline minus x squared

b. f (x) = x squared minus 3 x + 2

c. f (x) = StartRoot (x minus 2) EndRoot

d. f(x) = |x|