I went through Manhattan GMAT Guide #3 Chapter 5 - Function where I found Question #2 in the Problem Set a little confusing. The question says:
If g(x) = 3x+x^(1/2), what is the value of g(d^2 + 6d + 9).
In this case, the solution says:
g(d^2 + 6d + 9) = 3(d^2 + 6d + 9)+ (d^2 + 6d + 9)^1/2
3d^2 +18d+27 + sq.rt [(d+3)^2]
3d^2 +18d+27 + d+3 OR 3d^2 +18d+27 -(d+3)
3d^2 +19d+30 OR 3d^2 +19d+24
(if d+3 >=0) OR (if d+3 <=0) [Didn't understand this part quite well]
Other question is: if we are considering + and - signs while taking roots, why are we not taking them into consideration in Question 4 of the same exercise.
Could anyone please clarify from Manhattan GMAT faculty?