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