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Consider f:R^+to[-5, infty) given by f...

Consider `f:R^+to[-5, infty)` given by
`f(x)=9x^2+6x-5`. Show that f is invertible with `f^-1(y)=frac(sqrt(y+6)-1)(3)`

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

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  2. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

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  3. Consider f:R^+to[-5, infty) given by f(x)=9x^2+6x-5. Show that f is ...

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  4. Let f : X rarr Y be invertible, show that f has unique inverse

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  5. Consider f : {1, 2, 3} rarr {a, b, c} given by f(1) = a, f(2) = b and ...

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  6. Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, ...

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  7. If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) i...

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  8. f : R - {(-4)/3} rarr R be a function defined as f(x) = (4x)/(3x +4). ...

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  9. Can you define a function from 'RxR rarr R' such as 'f3: RxR rarr, R' ...

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  10. Can yóu define a function from 'R xx R rarr R' such as 'f4: R xx R rar...

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  11. Show that addition, subtraction and multiplication are binary opera...

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  12. Show that subtraction and division are not binary operations on N.

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  13. Show that *: R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binar...

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  14. Let P be the set of all subsets of a given set X. Show that uu: P xx P...

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  15. Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and t...

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  16. Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binar...

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  17. Show that *: R xx R rarr R defined by a * b=a+2 b is not commutative.

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  18. Show that addition and multiplication are associativé binary operation...

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  19. Show that * :R xx R rarr R given by a* b= a+2 b is not associative.

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  20. Show that zero is the identity for addition on R and 1 is the identity...

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