CAT 1999 — QA Question 36
Composite FunctionsEasy
Passage / Data
Directions: Answer the questions based on the following information.
Let x and y be real numbers and let
f (x,y) = |x + y| , F(f (x,y)) = −f (x,y)
and G(f (x, y)) = −F(f (x, y))
What is the value of f(G(f(1, 0)), f(F(f(1, 2)), G(f(1, 2))))?
Answer & solution
- A
3
- B
2
1
- D
0
Solution
f (x,y) = |x + y| This is always positive
F(f (x,y)) = − f (x,y) = −|x + y| This is always negative
G(f (x,y)) = − F(f (x,y)) = − (−|x + y|) = |x + y| This is always positive.
ƒ(G(ƒ(1, 0)), ƒ(F (ƒ(1,2)), G(ƒ(1, 2))))
= ƒ(G(ƒ(1, 0)), ƒ(3, − 3))
= ƒ(G(ƒ(1, 0)), 0)
= ƒ(−1, 0) = 1.