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Show that if f1a n df1 are one-one ma...

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.

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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 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.

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.

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): RvecR is given by ((f_1)/(f_2))(x)=(f_1(x))/(f_2(x)) for all xRdot

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

Suppose f_1 and f_2 are non-zero one-one functions from R to R . Is (f_1)/(f_2) necessarily one-one? Justify your answer. Here, (f_1)/(f_2): R->R is given by ((f_1)/(f_2))(x)=(f_1(x))/(f_2(x)) for all x in R .

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Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for every xgeq2 , is onto but not one-one.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A be any non-empty set. Then, prove that the identity function on ...

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

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

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

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

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  7. If the function fa n dg are given by f={(1,2),(3,5),(4,1)}a n dg="("(2...

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  8. Suppose f1a n df2 are non=zero one-one functions from RtoRdot is (f...

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  9. Find whether the following functions are one-one or not: f: Rvecgi...

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  10. If the function f and g are given by f={(1,2),(3,5),(4,1)} and g={(2,...

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  11. Discuss the surjectivity of the following functions: f: R-> given by ...

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  12. Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z ...

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  13. Let A be the set of all 50 students of class XII in a central school. ...

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  14. Show that the function f: RvecR defined by f(x)=3x^3+5 for all x in R...

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  15. Show that the function f: RvecR given by f(x)=cosxfora l lx in R , is...

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  16. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

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  17. If f(x) = x/(sqrt(1+x^2) then fofof(x)

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  18. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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

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  20. Let f: R-R be a function given by f(x)=a x+b for all x in R . Find th...

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