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Let S = {1, 2, 3}. Determine whether the...

Let `S = {1, 2, 3}`. Determine whether the functions `f : S->S`defined as below have inverses. Find `f^(-1)`, if it exists.(a) `f = {(1, 1), (2, 2), (3, 3)}`(b) `f = {(1, 2), (2, 1), (3, 1)}

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let f: R->R be defined as f(x)=x^2+1 . Find: f^(-1)(10)

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  2. If A={1,\ 2,\ 3,\ 4} , B={2,\ 4,\ 6,\ 8} and f: A->B is given by f(x)=...

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  3. Let S = {1, 2, 3}. Determine whether the functions f : S->Sdefined as ...

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  4. Consider f : {1, 2, 3}->{a , b , c}given by f(1) = a, f(2) = band f(3)...

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  5. If f:R-R is defined by f(x)=2x+7. Prove that f is a bijection. Also,...

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  6. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

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  7. Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and he...

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  9. Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ ...

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  10. Prove that the function f: R->R defined as f(x)=2x-3 is invertible....

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  11. Show that the function f: R ->R is given by f(x)=1+x^2 is not invertib...

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  12. Show that f: R-{-1}->R-{1} given by f(x)=x/(x+1) is invertible. Also, ...

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  13. Show that f: [-1, 1] ->R, given by f(x)=x/((x+2)is one- one . Find th...

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  14. Let f: R vec be defined as f(x)=10 x+7. Find the function g: RvecR su...

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  15. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

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  16. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

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  17. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , wher...

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  18. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

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  19. Let f : N ->Rbe a function defined as f(x)=4x^2+12 x+15. Show that f ...

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  20. State with reason whether following functions have inverse (i) f:{1,2...

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