GATE 2018 EE GA Q.5: solution and answer

GATE 2018 · EEGA Q.5 · 1 mark · MCQ

Functions $F (a, b)$ and $G (a, b)$ are defined as follows:
$F (a, b) = (a - b)^{2}$ and $G (a, b) = ∣ a - b ∣$ , where $∣ x ∣$ represents the absolute value of $x$ .
What would be the value of $G (F (1, 3), G (1, 3))$ ?

(A)
2
(B)
4
(C)
6
(D)
36

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Answer and solution

ANSWER

$G (F (1, 3), G (1, 3)) = G (4, 2) = ∣4 - 2∣ = 2$ , so the answer is option (A).

Official answer: ASource: Official answer key, GATE 2018 EE (IIT Guwahati)

Work from the inside out: evaluate both inner function values first, then feed them into the outer $G$ .
Inner $F$ : $F (1, 3) = (1 - 3)^{2} = (- 2)^{2} = 4$ (squaring a negative number gives a positive result).
Inner $G$ : $G (1, 3) = ∣1 - 3∣ = ∣ - 2∣ = 2$ (the absolute value drops the sign).
Outer $G$ , with $a = F (1, 3) = 4$ and $b = G (1, 3) = 2$ : $G (4, 2) = ∣4 - 2∣ = 2$
So $G (F (1, 3), G (1, 3)) = 2$ , which is option (A).

KEY IDEA

In a composite function, evaluate the innermost calls first. Each result then becomes an argument of the outer function, in the same position: the first argument is $a$ and the second is $b$ .

WATCH OUT FOR

Stopping at the inner value $F (1, 3) = 4$ and picking (B), or squaring at the outer level as well, e.g. computing $F (4, 2)$ or $(4 - 2)^{2}$ , or mixing up which function goes outside. Another slip is forgetting the absolute value, which only matters when the order of the arguments is reversed; here $4 - 2$ is already positive.

From the GATE 2018 EE paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

GATE 2018 EE GA Q.5: solution and answer

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