Playing with Graphs --- 4

Calculus Level 5

f ( x ) = { sin ⁡ ( x ) } − ∣ log ⁡ 10 ( 2 x − π + 2 2 ) ∣ f (x) = \{ \sin(x) \} - \left | {\log}_{10} \left( \dfrac{2x - \pi + 2}{2} \right) \right |

Find the number of roots of the following equation above.

Notation : { ⋅ } \{ \cdot \} denotes the fractional part function .

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2 6 0 4 7 3 5 8

Aniket Sanghi by Aniket Sanghi , 21, India

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1 solution

Aniket Sanghi
Feb 20, 2017

So Here is the Graphing of this graph

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I got 7 solutions only

A Former Brilliant Member - 3 years, 3 months ago

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For x=pi/2 fractional part of sin x is 0 and also the value of that log function is zero. So 1 point here and rest graph intersects at 7 points. so total roots are 8

kishan sharma - 3 years, 3 months ago

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thank you I got where I had made the mistake

A Former Brilliant Member - 3 years, 3 months ago

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