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If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R...

If `f(x+1/2)+f(x-1/2)=f(x)fora l lx in R ,` then the period of `f(x)` is (a) 1 (b) 2 (c) 3 (d) 4

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CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

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  2. Plot y=|x|,y=|x-2|, and y=|x+2|

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  3. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

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  4. If for all real values of ua n dv ,2f(u)cosv=f(u+v)+f(u-v), prove that...

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  5. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

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  6. If f: X rarr[1,oo) is a function defined as f(x)=1+3x^3, find the su...

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  7. Find the period (if periodic) of the following function ([.] denotes ...

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  8. Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer...

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  9. The domain of f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c), where a >0, b^2-4ac=0,...

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  10. If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

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  11. Discuss the continuity of f(x)=sgn(x^3-x)

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  12. If f(x)=x^2 for xgeq1 and x for x<0,then fof(x) is given by

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  13. If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(...

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  14. Let f: RrarrR, where f(x)=sinx , Show that f is into.

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  15. Draw the graph of the function: f(x)=log|x|

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  16. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, t...

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  17. Find the domain of f(x)(sqrt((1-sinx)))/((log)5(1-4x^2) +cos^(-1)(1...

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  18. Sketch the curve |y|=(x-1)(x-2)dot

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  19. If f(x) is a real-valued function defined as f(x)=In (1-sinx), then t...

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  20. Find the range of f(x)=cos((log)e{x})dot

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