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Let f(x)={(1, x in Q), (0, x in R-Q):} a...

Let f(x)=`{(1, x in Q), (0, x in R-Q):}` and g(x)=`{(1, x in R-Q), (0, x in Q):}`, find (f+g)(x) and (fg)(x).

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. Express each of e^x function as the sum of an even function and an odd...

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  2. Express each of x^2 function as the sum of an even function and an odd...

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  3. Let f(x)={(1, x in Q), (0, x in R-Q):} and g(x)={(1, x in R-Q), (0, x ...

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  4. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  5. Determine if the binaary operation o on the set R of real numbers defi...

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  6. On the set R of real numbers, a binary operation o is defined by a0b=a...

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  7. Find the idenity and inverse if any for the binary operation ** on Q-{...

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  8. Find the identity elements if any for the binary operations defined by...

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  9. Find the identity elements if any for the binary operations defined by...

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  10. Let f:Rto(-1,1) be defined by f(x)=x/(1+x^2),x in R. Find f^(-1) if ex...

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  11. Show that AxxA is an equivalence relation on a non-empty set A. What i...

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  12. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  13. Let R be the relation on Z defined by aRb iff a-b is an even integer. ...

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  14. Prove that cos tan^(-1)sin cot^(-1)x=sqrt((1+x^2)/(2+x^2).

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  15. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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  16. Prove that 2tan^-1(cosectan^-1x-tancot^-1x=tan^-1x.

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  17. Prove that 1/2cos^-1x=sin^-1sqrt((1-x)/2)=cos^-1sqrt((1+x)/2).

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  18. If cos^-1x+cos^-1y+cos^-1z=pi, prove that x^2+y^2+z^2+2xyz=1.

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  19. Slove: tan(cos^-1x)=sin(cot^-1""1/2)

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  20. Find the feasible region of the inequations x+2ylt8, 2x+ylt8 and xgt0,...

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