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Given examples of two one-one functio...

Given examples of two one-one functions `f_1a n df_2` from `R` to `R` such that `f_1+f_2: RvecR ,` defined by `(f_1+f_2)(x)=f_1(x)+f_2(x)` is not one-one.

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Give examples of two one-one functions f_1 and f_2 from R to R such that f_1+f_2: R->R , defined by (f_1+f_2)(x)=f_1(x)+f_2(x) is not one-one.

Show that if f_1a n df_1 are one-one maps from RtoR , then the product f_1xf_2: RvecR defined by (f_1xf_2)(x)=f_1(x)f_2(x) need not be one-one.

Show that if f_1a n df_2 are one-one maps from RtoR , then the product f_1×f_2: RtoR defined by (f_1×f_2)(x)=f_1(x)f_2(x) need not be one-one.

Show that if f_1 and f_2 are one-one maps from R to R , then the product f_1xxf_2: R->R defined by (f_1xxf_2)(x)=f_1(x)f_2(x) need not be one-one.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-one but not onto.

Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-one but not onto.

Prove that the function f:N to N , defined by f(x)=x^(2)+x+1 is one-one but not onto.

Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-one but not onto.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Show that if f1a n df2 are one-one maps from RtoR , then the produ...

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  2. Give examples of two surjective function f1 and f2 from Z to Z such...

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  3. Given examples of two one-one functions f1a n df2 from R to R such ...

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  4. If f: A->B and g: B->C are onto functions show that gof is ...

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  5. Show that the logarithmic function f: R0+vecR given by f(x)=(log)a ...

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  6. If f: AvecBa n dg: BvecC are one-one functions, show that gof is on...

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  7. If f: R->R be the function defined by f(x)=4x^3+7, show that f is a ...

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  8. Let A={1,2,3}dot Write all one-one from A to itself.

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

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

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

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

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

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

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

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

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

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

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

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

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