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

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`f(x) = x^2 + 2x – 3 and g(x) = 3x – 4`
Now,
`gof(x)=g(f(x))= g(x^2 + 2x – 3) `
`= 3(x^2 + 2x–3) – 4 `
`= 3x^2 + 6x – 9 – 4 `
` = 3x^2 + 6x – 13 `
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
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  2. 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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  3. 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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  4. 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={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(...

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

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

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

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

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

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

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

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

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

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

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

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

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