GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 2

The value of f∘g∘h(9) could be, if

f(x) = 1 /x
g(x) = 1 /(x−2)
h(x) = √x

(A) 3
(B) 1/3
(C) -5
(D) None of these.

Answer: (D)
Explanation:

fogoh(9) means f(g(h(9)))

Start by solving h(9) = √9 = 3 and not (3, -3) as square root of a number is always positive.
Taking the value to be 3,

g(3) = 1(3−2) = 1 
=> f(1) = 1

So, option (D) is correct.
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