CAT 2000 — QA Question 21
Basics (Functions)Easy
Passage / Data
Answer the following question based on the information given below.
For real numbers x, y, let
f(x, y) = Positive square-root of (x + y), if (x + y)0.5 is real
= (x + y)2, otherwise
g(x, y) = (x + y)2, if (x + y)0.5 is real
= –(x + y), otherwise
Under which of the following conditions is f(x, y) necessarily greater than g(x, y)?
Answer & solution
Both x and y are less than –1
- B
Both x and y are positive
- C
Both x and y are negative
- D
y > x
Solution
If 1 > (x + y) > 0; f(x, y) > g(x, y) and if (x + y) < –1; f(x, y) > g(x, y).
If both x and y are less than –1, (x + y) will also be less than –1.
Hence, option (a).