m CAT Questions - Algebra: Compound functions

CAT Practice : Functions

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Competitive exams always have questions that have no clear starting point for solving them, but have an easy solution if you think the right way. This is one such question.

Compound functions

    Q.4: Consider functions f(x) = x2 + 2x, g(x) = and h(x) = g(f(x)). What are the domain and range of h(x)?


  • Correct Answer
    Domain: ( -∞, +∞), Range -[0, ∞]

Detailed Solution

h(x) = g(f(x)) = g(x2 + 2x) = = |x + 1|

This bit is very important, and often overlooked.

= 3, not ±3
If x2 = 9, then x can be ±3, but is only +3.

So, = |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, ∞)

Correct Answer: Domain: ( -∞, +∞), Range -[0, ∞]

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