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Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} an...

Consider `f:{1,\ 2,\ 3}->{a ,\ b ,\ c}` and `g:{a ,\ b ,\ c}->` {apple, ball, cat} defined as `f(1)=a ,\ \ f(2)=b ,\ \ f(3)=c ,\ \ g(a)=` apple, `g(b)=` ball and `g(c)=` cat. Show that `f,\ g\ a n d\ gof` are invertible. Find `f^(-1),\ g^(-1)` and `(gof)^(-1)` and show that `(gof)^(-1)=f^(-1)o\ g^(-1)` .

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Find f^(-1) if it exists: f: A->B where A={0,\ -1,\ -3,\ 2}; B= {-9,\ ...

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  2. Find f^(-1) if it exists: f: A->B where A={1,\ 3,\ 5,\ 7,\ 9}; B= {0,\...

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  3. Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} and g:{a ,\ b ,\ c}-> {apple, ba...

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  4. Let A={1,2,\ 3,\ 4};\ B={3,\ 5,\ 7,\ 9}; C={7,\ 23 ,\ 47 ,\ 79} and f:...

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  5. Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Als...

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  6. Consider f: R->Rgiven by f(x) = 4x + 3. Show that f is invertible. Fin...

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  7. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

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  8. If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show that fof(x)=x for all x!=2/3dot...

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  9. Consider f: R+->[-5,oo)given by f(x)=9x^2+6x-5. Show that f is inverti...

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  10. If f: R->R be defined by f(x)=x^3-3 , then prove that f^(-1) exists an...

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  11. A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not...

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  12. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

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  13. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

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  14. Consider f:R+->[-9,oo[ given by f(x)=5x^2+6x-9. Prove that f is invert...

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  15. Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: Nvec...

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  16. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

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  17. If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invert...

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  18. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

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  19. Let A={x in R|-1lt=xlt=1} and let f: A->A ,\ g: A->A be two functions...

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  20. Let f be a function from R to R such that f(x)=cos(x+2) . Is f inverti...

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