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Q. f={(x+a if x<0), (|x-1| if x>=0) g(...

Q. f={`(x+a if x<0)`, `(|x-1| if x>=0)` `g(x)={(x+1 if x<0),(x-1)^2 + b if x>=0)` where a and b are non-negative real numbers. Determine the composite function `gof`. If `(gof)(x)` is continuous for all real x, determine the values of a and b, Further for these values of a and b, is `gof` differentiable at x=0? Justify your answer.

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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
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  2. Let f be a continuous, g be a discontinuous function. Prove that f + g...

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  14. If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not diff...

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  15. Determine the values of x for which the following functions fails to b...

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  16. "If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1," prove...

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  17. Let alpha in R. Prove that a function f: RtoR is differentiable a...

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  19. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

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