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how to convert Piecewise function to normal function of one line like f(x)={ 2:x=0 ;; 1 : x>0 } f(x)=floor( (x+2) / (x+1) ) g(x)={ a : x=0 ;; b*a : x>0 } g(x)=a + (a-1)*b*( 2-f(x) )

how to convert Piecewise function to normal function of one line like
f(x)={   2:x=0 ;; 1 : x>0   }
f(x)=floor( (x+2) / (x+1) )
 
g(x)={   a : x=0 ;; b*a : x>0   }
g(x)=a  +  (a-1)*b*(  2-f(x)  )

Grade:12th pass

2 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
2 years ago

As Rect( (x-a)/b ) = H(x - a - b/2) - H(x - a + b/2) then your expression is exactly the same as that given above by @Christoforos. Hence, it still does not satisfy the BC at at x = 0; x = 0.5 and x = 1.
If you define G(x) = H(x) + H(- x²) then
f(x) = G(x) + G(x-1) - 2G(x-0.5
Rituraj Tiwari
askIITians Faculty 1792 Points
2 years ago

As Rect( (x-a)/b ) = H(x - a - b/2) - H(x - a + b/2) then your expression is exactly the same as that given above by @Christoforos. Hence, it still does not satisfy the BC at at x = 0; x = 0.5 and x = 1.
If you define G(x) = H(x) + H(- x²) then
f(x) = G(x) + G(x-1) - 2G(x-0.5

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