what is the domain of the step function ( f(x)=2x-1 )?\n( {x|xgeq - 1} )\n( {x|xgeq 1} )\n( {x|x ) is an…

what is the domain of the step function ( f(x)=2x-1 )?\n( {x|xgeq - 1} )\n( {x|xgeq 1} )\n( {x|x ) is an integer}\n( {x|x ) is a real number}

what is the domain of the step function ( f(x)=2x-1 )?\n( {x|xgeq - 1} )\n( {x|xgeq 1} )\n( {x|x ) is an integer}\n( {x|x ) is a real number}

Answer

Explanation:

Step1: Recall the definition of the domain

The domain of a function is the set of all possible input values (x - values) for which the function is defined.

Step2: Analyze the step - function (y = \lfloor 2x\rfloor-1)

The greatest - integer function (\lfloor t\rfloor) (where (t = 2x)) is defined for all real values of (t). Since (t = 2x) and (x=\frac{t}{2}), and there is no restriction on the value of (t) (because for any real number (t), (\lfloor t\rfloor) is well - defined), there is no restriction on the value of (x).

Answer:

({x|x\text{ is a real number}})