Find the domain of the function \(f(x) = \dfrac{1}{2 \sqrt{\sqrt{x} - x} - 1}\)

Guest Jun 9, 2020

#1**0 **

The domain of the function consists of all real numbers except those numbers that make the denominator equal to zero.

Let's try to find those numbers.

2·sqrt[ sqrt(x) - x ] - 1 = 0

2·sqrt[ sqrt(x) - x ] = 1

sqrt[ sqrt(x) - x ] = ½

sqrt(x) - x = ¼

-x + sqrt(x) - ¼ = 0

x - sqrt(x) + ¼ = 0

Using the quadratic equation: sqrt(x) = [ -(-1) +/- sqrt( (1)^{2} - 4·1·¼ ) ] / (2·1)

sqrt(x) = [ 1 + sqrt(0) ] / 2

sqrt(x) = ½

x = ¼

¼ is the number that cannot be included in the domain; so the domain consists of all real numbers except ¼.

geno3141 Jun 10, 2020