Answer:
[tex]f^{-1}(x)=(\frac{x}{6})^{\frac{1}{4}}[/tex]
This is a function for [0,∞).
Step-by-step explanation:
The given function is
[tex]f(x)=6x^4[/tex]
We need to find the [tex]f^{-1}(x)[/tex].
Step 1: Replace f(x) be y.
[tex]y=6x^4[/tex]
Step 2: Interchange x and y.
[tex]x=6y^4[/tex]
Step 3: Isolate variable y.
[tex]\frac{x}{6}=y^4[/tex]
[tex](\frac{x}{6})^{\frac{1}{4}}=y[/tex]
Step 4: Interchange the sides.
[tex]y=(\frac{x}{6})^{\frac{1}{4}}[/tex]
Step 5: Replace y by [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)=(\frac{x}{6})^{\frac{1}{4}}[/tex]
Therefore, [tex]f^{-1}(x)=(\frac{x}{6})^{\frac{1}{4}}[/tex].
This function is is defined for all positive values of x.
The inverse of function [tex]f(x)=6x^4[/tex] is a function for [0,∞).
