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

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`

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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 .

Let f be a function from R to R such that f(x)=cos(x+2) . Is f invertible? Justify your answer.

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.

Let f be a one-one function satisfying f'(x)=f(x) then (f^-1)''(x) is equal to

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.

If f: RvecR is given by f(x)=(x^2-4)/(x^2+1) , identify the type of function.

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

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. 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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  16. If f(x)=e^x and g(x)=(log)e x(x >0), find foga n dgofdot Is fog=gof?

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  17. If f:[0,oo)vecRa n dg: RvecR be defined as f(x)=sqrt(x) and g(x)=-x^2-...

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  18. Let f and g be real functions defined by f(x)=x/(x+1) a n d g(x)=1/(x...

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  19. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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  20. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

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