CAT 2000 — QA Question 20
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
Which of the following expressions yields a positive value for every pair of non-zero real number (x, y)?
Answer & solution
- A
f(x, y) – g(x, y)
- B
f(x, y) – (g(x, y))2
- C
g(x, y) – (f(x, y))2
f(x, y) + g(x, y)
Solution
If (x + y) > 0, (x + y)0.5 is real.
∴ For (x + y) > 0;
f(x, y) = Positive square-root of (x + y) > 0
g(x, y) = (x + y)2 > 0
Otherwise,(i.e. for (x + y) < 0);
f(x, y) = (x + y)2 > 0
g(x, y) = –(x + y) > 0
Now it is clear that f(x, y) + g(x, y) will always be positive.
Hence, option (d).