The number of elements in the set S= {x∈R : 2cos\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}
- 1
- 3
- 0
- infinite
The Correct Option is A
Solution and Explanation
S={x∈R:2cos\((\frac{x_2+x}{6})=4^x+4^{-x}\)}
L.H.S. is less than or equal to 2 and RHS is greater than or equal to 2.
So equality holds only if LHS = RHS = 2
R.H.S. is 2 when x = 0
and at x = 0, LHS is also 2.
So, only one solution exist.
Therefore, the correct option is (A): 1.
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Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
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Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
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Cardinal Number of a Set:
The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
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