Question

Find the range of the real valued function: f(x) = $\sqrt{[x] - x}$

Answer 1

Answer:

range (f) =(1,∞)

Step-by-step explanation:

Find the range of the real valued function:

$f(x)=\sqrt{[x]-x}$

[x] is greatest integer function which gives less than or equal to x.

let

$y=\sqrt{[x]-x}$

=> 0 < [x]-x < 1  for all x∈ R-Z

=> 1 ≤ f(x) < ∞

so range (f) =(1,∞)