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f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} a...

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

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`h(x)={(sin^2x-sinx+1, -1 ltx lt0),(2sin^2x, 0ltxle1):}`
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PATHFINDER-FUNCTION-QUESTION BANK
  1. 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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  2. Let f(x) be defined on [-2,2] and is given by f(x)={(-1, -2lexlt0),(x...

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

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

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

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

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

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

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

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

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

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

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

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  14. If f(X)=lim[x/(x+1) + x/{(x+1)(2x+1)} + x/{(2x+1)(3x+1)} +…+ to n term...

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  15. Find the range of the following function f(x)=log2"((sinx-cosx+3sqrt2...

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  16. If - pi/2 lt x lt pi/2, then the range of the function f(x)=cos [x] i...

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  17. If f : R rarr R is defined by f(x)=1/(2-cos3x) for each x in R, then t...

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  18. If f(x+y)=f(x)f(y)AA x,y in R, f(0) ne 0 then F(x) = {f(x)/(1+(f(x)))^...

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  19. A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R ...

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  20. If the function f(x)=[3.5 + b sin x] (where[.] denotes the greatest in...

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