Question

Find g(2/3). Simplify your answer. Type an exact answer, using radicals as needed).

Answer 1

The solution is 2sqrt77/77.  You just fill in 2/3 for the x's. When you do that, you do that you get (2/3)/sqrt(9-[2/3]^2) which, simplified, is (2/3)/sqrt(9-[4/9]). Now use the common denominator under the radical of 9 to get (2/3)/sqrt([81-4]\9).  Simplifying even further gives you (2/3)/([sqrt(77)]/3). Now do that division by multiplying 2/3 by the reciprocal of ([sqrt(77)]/3) to get 2/sqrt77.  I rationalized the denominator to get that result up there.