The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).
In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.
The function can be shown as:
y = f(x) = x⁴,
or, x⁴ = y,
or, [tex]x = \pm\sqrt[4]{y}[/tex]
Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].
Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
Learn more about inverse functions at
https://brainly.com/question/21927534
#SPJ1
The complete question is:
"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?
A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]
B. [tex]F(x)= \sqrt[4]{x}[/tex]
C. [tex]F(x)= \pm x^4[/tex]
D. [tex]F(x)=- \sqrt[4]{x}[/tex] "
