UGC-NET January 2017 Paper-2 Discrete Maths Questions Solved

3. Q:: 3  The functions mapping R into R are defined as: f(x) =  and h(x) = .

Then find the value of the following composite functions: hog(x) and hogof(x)

(1)        and     
(2)        and     
(3)      and    
(4)      and   

Answer:: (4)

Explanation::

hog(x) = h(g(x)) = (1/(x^2+1))^4 = (x^2 + 1)^-4

hogof(x) = ho(g(f(x))) = 

Now g(f(x)) = 1/((x^3-4x)^2 + 1)

h(g(f(x))) = h(1/((x^3-4x)^2 + 1)) = (1/((x^3-4x)^2 + 1))^4 

= ((x^3-4x)^2 + 1)^-4

Hence  hog(x) = (x^2 + 1)^-4 and hogof(x) =  ((x^3-4x)^2 + 1)^-4

So correct answer is (D)

UGC-NET January 2017 Paper-2 discrete maths questions with solution

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