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Let A="{"-1,0,1")"a n df={(x , x^2): xA}...

Let `A="{"-1,0,1")"a n df={(x , x^2): xA}dot` Show that `f: AvecA` is neither one-one nor onto.

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To show that the function \( f: A \to A \) defined by \( f(x) = x^2 \) is neither one-one nor onto, we will follow these steps: ### Step 1: Define the Set A and the Function Let \( A = \{-1, 0, 1\} \) and the function \( f(x) = x^2 \) for \( x \in A \). ### Step 2: Calculate the Function Values We will calculate the function values for each element in the set \( A \): - For \( x = -1 \): ...
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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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