Functions 2 Question 14

15. Let g(x) be a function defined on [1,1]. If the area of the equilateral triangle with two of its vertices at (0,0) and [x,g(x)] is 3/4, then the function g(x) is

(1989, 2M)

(a) g(x)=±1x2

(b) g(x)=1x2

(c) g(x)=1x2

(d) g(x)=1+x2

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Answer:

Correct Answer: 15. (a,b,c)

Solution:

  1. Since, area of equilateral triangle =34(BC)2

34=34[x2+g2(x)]g2(x)=1x2

g(x)=1x2 or 1x2

Hence, (b) and (c) are the correct options.



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