Assertion :Let f:[8π,9π]→[−1,1],f(x)=cosx, then Statement-1 : f−1(−1)=9π because Reason: Statement-2 : f−1(x)=10π−cos−1x∀x∞[−1,1]
A
Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1
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B
Statement-1 is true, Statement-2 is true and Statement-2 is NOT correct explanation for Statement-1
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C
Statement-1 is true, Statement-2 is false
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D
Statement-1 is false, Statement-2 is true
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Solution
The correct option is C Statement-1 is true, Statement-2 is false f(x)=cos(x). f−1(−1)=9π cos(π)=cos(9π) domain of cos−1x is [-1,1] range of cos−1xis[0,π] in the question given the domain specified is [9π,10π] always the inverse function value should be in the given range. statement 1 is true. statement 2 is false. f−1(x)=8π+cos−1x