Find the domain restriction for the function f(x) = (2x-5)^4. use an inequality to state the domain.

On function f(x) there is no domain restriction all real numbers are in the domain of f(x).

Step-by-step explanation:

x∈R (set of all real numbers)

or in other words we can write the domain of x as -∞<x<+∞

Given equation: f(x)=(2x-5)^4

when;

x=-2: f(-2)=(2(-2)-5)^4 =(-4-5)^4 =(-9)^4 =[(-1)^4]*[(9)^4] =(9)^4=6561

x=-1: f(-1)=(2(-1)-5)^4 =(-2-5)^4 =(-7)^4 =[(-1)^4]*[(7)^4] =(7)^4=2401

x=0: f(0)=(2(0)-5)^4 =(0-5)^4 =(-5)^4 =[(-1)^4]*[(5)^4] =(5)^4=625

x=1: f(1)=(2(1)-5)^4 =(2-5)^4 =(-3)^4 =[(-1)^4]*[(3)^4] =(3)^4=81

x=2: f(1)=(2(2)-5)^4 =(4-5)^4 =(-1)^4 =1

The value of given function is decreasing rapidly when the value of x increases.