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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|
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