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March 12, 2024Theory-of-Computation
March 12, 2024UGC NET CS 2017 Jan -paper-2
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Question 3
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The functions mapping R into R are defined as : f(x) = x 3 – 4x, g(x) = 1/(x 2 + 1) and h(x) =
x 4 . Then find the value of the following composite functions : hog(x) and hogof(x)
x 4 . Then find the value of the following composite functions : hog(x) and hogof(x)
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(x 2 + 1)4 and [(x 3 – 4x) 2 + 1] 4
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(x 2 + 1)4 and [(x 3 – 4x) 2 + 1] -4
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(x 2 + 1)-4 and [(x 3 – 4x) 2 + 1] 4
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(x 2 + 1)-4 and [(x 3 – 4x) 2 + 1] -4
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Question 3 Explanation:
Step-1: Given data,
f(x) = x 3 – 4x, g(x) = 1/(x 2 + 1) and h(x) = x 4
hog(x)=h(1/(x 2 + 1))
=h(1/(x 2 )+1) 4
= 1/(x 2 +1) 4
= (x 2 +1) -4
hogof(x)= hog(x 3 -4x)
= h(1/(x 3 -4x) 2 +1)
= h(1/(x 3 -4x) 2 +1) 4
= h((x 3 -4x) 2 +1) -4
So, option D id is correct answer.
f(x) = x 3 – 4x, g(x) = 1/(x 2 + 1) and h(x) = x 4
hog(x)=h(1/(x 2 + 1))
=h(1/(x 2 )+1) 4
= 1/(x 2 +1) 4
= (x 2 +1) -4
hogof(x)= hog(x 3 -4x)
= h(1/(x 3 -4x) 2 +1)
= h(1/(x 3 -4x) 2 +1) 4
= h((x 3 -4x) 2 +1) -4
So, option D id is correct answer.
Correct Answer: D
Question 3 Explanation:
Step-1: Given data,
f(x) = x 3 – 4x, g(x) = 1/(x 2 + 1) and h(x) = x 4
hog(x)=h(1/(x 2 + 1))
=h(1/(x 2 )+1) 4
= 1/(x 2 +1) 4
= (x 2 +1) -4
hogof(x)= hog(x 3 -4x)
= h(1/(x 3 -4x) 2 +1)
= h(1/(x 3 -4x) 2 +1) 4
= h((x 3 -4x) 2 +1) -4
So, option D id is correct answer.
f(x) = x 3 – 4x, g(x) = 1/(x 2 + 1) and h(x) = x 4
hog(x)=h(1/(x 2 + 1))
=h(1/(x 2 )+1) 4
= 1/(x 2 +1) 4
= (x 2 +1) -4
hogof(x)= hog(x 3 -4x)
= h(1/(x 3 -4x) 2 +1)
= h(1/(x 3 -4x) 2 +1) 4
= h((x 3 -4x) 2 +1) -4
So, option D id is correct answer.