Compute the domain of the real-valued function f(x) = sqrt(3 + sqrt(5 + sqrt(x)).
+1632 \(f(x)=\sqrt{3 + \sqrt{5 + \sqrt{x}}}\)
\(x\ge0\)
Smallest value of the function would be \(\sqrt{3 + \sqrt{5}}\)
Maximum value is infinity.
\(a + b\sqrt{c} = \sqrt{3 + \sqrt{5}}\)
\(a + b\sqrt{5} = \sqrt{3 + \sqrt{5}}\)
(a + bsqrt(5))^2 = 3 + sqrt(5)
a^2 + 5b^2 + 2absqrt(5) = 3 + sqrt(5)
a^2 + 5b^2 = 3
sqrt(5) = 2absqrt(5)
2ab = 1
ab = 1/2
You can do it from here... Domain: [a + bsqrt(c), inf)
Get a and b, or just use the sqrt(3 + sqrt(5))
