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A function is defined for all real numbe...

A function is defined for all real numbers is defined for `xgt0` as follows:
`f(x)={(x|x|, 0lexlt1), (2x, xge1):}`
How is f defined for `xle0`
If f is odd

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`f(x)={(-x|x|, -1ltx le0),(2x, xle-1):}`
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PATHFINDER-FUNCTION-QUESTION BANK
  1. Determine whether even or odd: f(x)=x((a^x+1)/(a^x-1))

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  3. A function is defined for all real numbers is defined for xgt0 as foll...

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  4. Show that the function f(x)=(2x(sinx+tanx))/(2[(x+21pi)/pi]-41) is sym...

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  5. Find the period of following function f(x)=[sin3x]+[cos6x]

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  6. Find the period of following function f(x)=1/2{|sinx|/cosx+|cosx|/sin...

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  7. Find the period of following function f(x)=e^(ln(sinx))+tan^3x-"cosec...

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  8. Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where...

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  9. Let f(x) be defined on [-2,2] and is given by f(x)={(-1, -2lexlt0),(x...

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  10. f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} and g(x)=sin x. Then find h(x)=...

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  11. Find the inverse of the following function: f(x)=sin^(-1)(x/3), x in [...

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  12. Find the inverse of the following function: f(x)=loge(x^2+3x+1), x in ...

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  13. Find the inverse of the following function: f(x)=loge(x+sqrt(x^2+1))

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  14. If the function f:[1, infty) rarr [1, infty) is defined by f(x)=2^(x(x...

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  15. f(x)=sin^(-1)(x-1)+cos^(-1)(x-2), then domain of f(x) is

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  16. The domain of definition of the function y(x) given by the equation 2^...

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  17. Domain of the function f(x)=1/sqrt(^10C(x-1) -3. ^10Cx contains the po...

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  18. Domain of the function f(x)=x/sqrt(sin(Inx)-cos(Inx)) is

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  19. If f(X)=sqrt(sec^-1((2-|x|)/4)), then the domain of f(x) is

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  20. The range of the function f(x)=sin^-1(log [x])+log(sin^-1[x]), (where...

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