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Exploring the Family of Functions: f(x) = log(x)½ and its Variations

This document delves into the family of functions derived from f(x) = log(x)½, examining various transformations and their implications. We explore functions such as g(x) = f(x) + 1, g(x) = f(x) - 1, and their respective graphical representations. Additionally, we discuss scaling, shifting, and reflections of the logarithmic function, such as g(x) = f(cx) and g(x) = f(x - 1). The relationships and properties of these functions reveal insights into logarithmic behavior and transformations in mathematical analysis.

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Exploring the Family of Functions: f(x) = log(x)½ and its Variations

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  1. Serial No: 32

  2. The family of the f(x)=log x ½

  3. f(x) = log x ½ y x 1

  4. y g(x)=f(x)+1= log x + 1½ x 2

  5. g(x)=f(x)-1 = log x - 1 ½ y x 1/2

  6. g(x)=f(cx) = log cx ; c=2 ½ y x 1/2

  7. y y=cf(x) = clog x ; c=2 ½ 2 x 1 1/2

  8. g(x)=f(x-1) = log (x-1) ½ X=1 2

  9. y=f(x+1) = log (x+1)½ X=-1

  10. g(x) =f(-x) = log( - x) ½ y x -1

  11. g(x) =-f(x)= - log x ½ y x 1

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