Domain of the function ; f(x) = √(1-√(x^2-4x+5)) is

(1) R

(2) R-{2}

(3) {2}

Asked by rishijuneja2018 | 29th Jun, 2019, 05:32: PM

Expert Answer:

f(x) = √(1 - √(x- 4x + 5))
Consider,
x- 4x + 5 = x- 4x + 4 + 1 
                 = (x - 2)2 + 1
Hence,
1 - √(x- 4x + 5) ≥ 0
1 - √[(x - 2)2 + 1] ≥ 0
then
(x - 2)2 ≤ 0
x - 2 ≤ 0
Hence, function is defined only for x = 2
Correct option is (3)

Answered by Sneha shidid | 1st Jul, 2019, 12:38: PM