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Examine f:R rarr R, f(x) =|x| functions ...

Examine `f:R rarr R, f(x) =|x|` functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

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ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS ( Exercise 1 (b))
  1. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

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  2. Examine f:R rarr R, f(x) = [x] ="the greatest integer" le x. function...

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  3. Examine f:R rarr R, f(x) =|x| functions if it is (i) injective (ii) s...

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  4. Examinef: R rarr R, f(x) ="sgn" x functions if it is (i) injective (i...

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  5. Examine f:R rarr R, f = id R="the identity function or R."functions i...

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  6. Show that the functions are injective f(x) = sinx on [ 0, (pi)/(2)...

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  7. Show thatf(x)= cos x [0 , pi] functions are injective.

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  8. Show that f(x) = loga x "on" (0,oo ),(a gt 0 "and" a != 1) functions a...

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  9. Show that the function f(x)=a^(x), x in R is injective, where (a gt 0 ...

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  10. Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 a...

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  11. Give an example of a function which is Surjective but not injective.

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

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  13. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  14. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  15. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

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  16. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  17. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

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  18. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

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  19. Find the composition fog and gof and test whether fog = gof when f and...

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  20. Find the composition fog and gof and test whether fog = gof when f and...

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