The question is about Compound functions. We need to find out the domain and range of a function of a function that is called a compound function. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.
Question 3: 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)?
h(x) = g(f(x)) = g(x2 + 2x) = √(x2 + 2x + 1) = √(x + 1)2 = |x + 1|
This bit is very important, and often overlooked.
√(9) = 3, not ±3
If x2 = 9, then x can be ±3, but √(9) is only +3.
So, √(x2) = |x|, not +x, not ±x
Domain of |x + 1| = ( -∞, +∞), x can take any value.
As far as the range is concerned, |x + 1| cannot be negative. So, range = [0, ∞)
The question is "What are the domain and range of h(x)?"
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