What if 0 b 1 consider g x 1 2 we could certainly

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f the basic properties of radicals from Intermediate Algebra.1 Definition 5.4. Let x be a real number and n a natural number.a If n is odd, the principal √ √n √ nth root of x, denoted n x is the unique real number satisfying ( n x) = x. If n is even, n x is √ defined similarlyb provided x ≥ 0 and n x ≥ 0. The index is the number n and the radicand is √ √ the number x. For n = 2, we write x instead of 2 x. a b Recall this means n = 1, 2, 3, . . .. √ Recall both x = −2 and x = 2 satisfy x4 = 16, but 4 16 = 2, not −2. √ It is worth remarking that, in light of Section 5.2, we could define f (x) = n x functionally as the inverse of g (x) = xn with the stipulation that when n is even, the domain of g is restricted to [0, ∞). From what we know about g (x) = xn from Section 3.1 along with Theorem 5.3, we can produce √ the graphs of f (x) = n x by reflecting the graphs of g (x) = xn across the line y = x. Below are the √ √ √ graphs of y = x, y = 4 x and y = 6 x. The point (0, 0) is indicated as a reference. The axes are hidden so we can see...
View Full Document

Ask a homework question - tutors are online