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Suppose f1a n df2 are non-zero one-one...

Suppose `f_1a n df_2` are non-zero one-one functions from `RtoRdot` is `(f_1)/(f_2)` necessarily one-one? Justify your answer. Here, `(f_1)/(f_2): RtoR` is given by `((f_1)/(f_2))(x)=(f_1(x))/(f_2(x))` for all `x∊Rdot`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A={1,2,3}dot Write all one-one from A to itself.

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  2. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor on...

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  3. Suppose f1a n df2 are non-zero one-one functions from RtoRdot is (f1...

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  4. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g ={(1,\ 3),\ (3,\ 3),\ (4,\...

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  5. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

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  6. Let f: RvecR and g: RvecR be defined by f(x)=x^2 and g(x)=x+1. Show ...

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  7. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

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  8. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

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  9. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

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  10. Show that the exponential function f: R to R , given by f(x)=e^x , i...

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  11. Let A="{"-1,0,1")"a n df={(x , x^2): xA}dot Show that f: AvecA is neit...

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  12. If f: AvecB is an injection such that range of f={a}dot Determine t...

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  13. Which of the following functions from AtoB are one-one and onto? ...

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  14. Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-on...

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  15. Let A be any non-empty set. Then, prove that the identity function on ...

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  16. Let A=R-[2] \ a n d \ B=R-[1]. If f: A->B is a mapping defined by f(x)...

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  17. Show that if f1a n df1 are one-one maps from RtoR , then the pro...

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  18. Give examples of two one-one functions f1 and f2 from R to R such t...

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  19. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

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  20. If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given ...

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