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Prove that f: (-1,1) rarr R defined by: ...

Prove that `f: (-1,1) rarr R` defined by:
`f(x) = {((x)/(1+x),-1 lt x lt 0),(0,x= 0),((x)/(1-x),0 lt x lt 1):}` is bijective. Prove that f is one -one onto

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Revision Exercise
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  2. Let R be a relation from N to N defined by R = {(a , b) : adot b in ...

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  4. If f(x)=log((1+x)/(1-x)) show that f((2x)/(1+x^2))=2(f(x))

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  5. If f(x)=(2x)/(1+x^2)\ , show that f(tantheta)=sin2theta)

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  6. यदि f(x) = "log"(e)x, तो सिद्ध कीजिए की f(x y z) = f(x) + f(y) + f(z)

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  7. If for non-zero x, if f(x) + mf ((1)/(x)) = (1)/(x) -5, where 1 ne m, ...

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  8. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  9. Period of f(x) = sin^4 x + cos^4 x

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  12. Find the domain of F (x) = (1)/(x) + 2^(sin^(-1)x) + (1)/(sqrt(x-2))

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  14. Find the domain and range of the following functions: (i) f(x) = (1)...

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  15. Is the function: f(x) = (x^(2) - 8x + 18)/(x^(2) + 4x + 30) one-one?

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  16. Prove that f: (-1,1) rarr R defined by: f(x) = {((x)/(1+x),-1 lt x l...

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  17. Let f: N->N be defined by: f(n)={n+1,\ if\ n\ i s\ od d n-1,\ if\ n\ i...

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  18. Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1...

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