Questions from functions have increased over the past few years. Given below is an interesting question from functions.
Consider functions f(x) = x2 + 2x, g(x) = √(x +1) and h(x) = g(f(x)). What are the domain and range of h(x)?
Domain = ( – infinity, +infinity)
Range – [0, infinity]
h(x) = g(f(x)) = g(x2 + 2x) = Ö( x2 + 2x + 1) = Ö(x+1)2 = | x + 1|
This bit is very important, and often overlooked
sqrt(9) = 3, not +3
If x2 = 9, then x can be +3, but Sqrt(9) is only +3.
So, Sqrt(x2)= |x|, not +x, not + x
Domain 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)