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Find `gof` and `fog` when `f: R->R` and `g: R->R` is defined by `f(x)=x` and `g(x)=|x|`

Text Solution

Verified by Experts

`f(x)=x`
and `g(x)=|x|`
So,
`f(g(x))=f(|x|)=|x|`
`g(f(x))=f(x)=|x|`
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Find gof and gof when f: R->R and g: R->R is defined by f(x)=2x+x^2 an...

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  2. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

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  3. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x...

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  4. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 ...

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  5. Find gof and gof when f: R->R and g: R->R is defined by f(x)=8x^3 and ...

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  6. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and ={(1,\ 3),\ (3,\ 3),\ (4,\ 9...

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  7. Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(...

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  8. Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and let f and g be two functions f...

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  9. Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(...

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  10. Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R...

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  11. Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show tha...

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  12. Let f: RvecR and g: RvecR be defined by f(x)=x+1 and g(x)=x-1. Show...

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  13. Verify assoiativity for the following three mappings : f: NvecZ0...

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  14. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

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  15. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  16. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  17. If f: AvecBa n dg: BvecC are one-one functions, show that gof is on...

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  18. If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sin...

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

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

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