How does it change?

Algebra Level 2

Consider f ( x ) = s i n ( x ) f\left( x \right) =sin(x) and other function h ( x ) = g ( x ) . f ( x ) h\left( x \right) =g\left( x \right) .f\left( x \right)

What should be g ( x ) g\left( x \right) . If the following holds true

  • h ( x ) = f ( x ) h\left( x \right) =f(x)\quad when x ≥ 0 x\ge 0

  • h ( x ) = 0 h\left( x \right) =0\quad when x<0

Note

  • x ∈ R x\in R\quad

  • sgn is sign(signum) function

  • abs is absolute value or |sinx|

g ( x ) = s g n ( tan ⁡ x ) + 1 2 g\left( x \right) =\frac { sgn(\tan { x) } +1 }{ 2 } g ( x ) = s g n ( cos ⁡ x ) + 1 2 g\left( x \right) =\frac { sgn(\cos { x) } +1 }{ 2 } g ( x ) = a b s ( s i n x ) s i n x g\left( x \right) =\frac {abs(sinx) }{ sinx } g ( x ) = s g n ( sin ⁡ x ) + 1 2 g\left( x \right) =\frac { sgn(\sin { x) } +1 }{ 2 }

Kandarp Singh by Kandarp Singh , 22, India

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1 solution

Kandarp Singh
Dec 9, 2017

Image Credit: Desmos Graphing Calculator

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