Questions from functions have increased over the past few years. Given below is an interesting question from functions.

Question

Consider functions f(x) = x^{2} + 2x, g(x) = √(x +1) and h(x) = g(f(x)). What are the domain and range of h(x)?

Correct Answers:

Domain = ( – infinity, +infinity)

Range – [0, infinity]

Explanatory Answer

h(x) = g(f(x)) = g(x

^{2}+ 2x) = Ö( x^{2}+ 2x + 1) = Ö(x+1)^{2}= | x + 1|This bit is very important, and often overlooked

sqrt(9) = 3, not

__+__3If x

^{2}= 9, then x can be__+__3, but Sqrt(9) is only +3.So, Sqrt(x

^{2})= |x|, not +x, not__+__xDomain of | x + 1| = ( -infinity, + infinity), x can take any value.

As far as the range is concerned, | x + 1| cannot be negative. So, range = [0, infinity)