Consider f(x)={x+[log2(2+x)]}+{x+[log2(2+x2)]}+...+{x+[log2(2+x10)]}, then correct statement is
(where {} and [] denotes the fractional part function and greatest integer function respectively)
A
[f(e)]=7
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B
f(π)=20π−60
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C
Number of solutions of the equation f(x)=x is 9
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D
Number of solutions of the equation f(x)=x is 10
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Solution
The correct option is C Number of solutions of the equation f(x)=x is 9 {x+[log2(2+x)]}={x+[log2(2+x2)]}=....={x+[log2(2+x10)]}=x ∴f(x)={x}+{x}+−−−−+{x} f(x)=10{x} f(e)=10{e}=10(e−2) ∴[f(e)]=7 f(π)=10(π−3) f(x)=x
So total number of solutions = 9