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Question
Number of values of x∈[0,π] where f(x)=[4sinx−7] is non-derivable is
[Note: [k] denotes the greatest integer less than or equal to k.]
Number of values of x∈[0,π] where f(x)=[4sinx−7] is non-derivable is
[Note: [k] denotes the greatest integer less than or equal to k.]
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Solution
The correct option is B 8
f(x)=[4sinx−7]f(x) is derivable, if f is definedNow, f is defined if [4sinx−7] is definedWe know that,
−1≤sinx≤1 for 0≤x≤2π
−4≤4sinx≤4
−11≤4sinx−7≤−3
[4sinx−7]=−11,−10,−9,−8,−7,−6,−5,−4
Total 8 number
f(x)=[4sinx−7]
f(x) is derivable, if f is defined
Now, f is defined if [4sinx−7] is defined
We know that,
−1≤sinx≤1 for 0≤x≤2π
−4≤4sinx≤4
−11≤4sinx−7≤−3
[4sinx−7]=−11,−10,−9,−8,−7,−6,−5,−4
Total 8 number
−1≤sinx≤1 for 0≤x≤2π
−4≤4sinx≤4
−11≤4sinx−7≤−3
[4sinx−7]=−11,−10,−9,−8,−7,−6,−5,−4
Total 8 number
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