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If f: R->R and g: R->R be functions defi...

If `f: R->R` and `g: R->R` be functions defined by `f(x)=x^2+1` and `g(x)=sinx ,` then find `fog` and `gof` .

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Verified by Experts

Given `f(x)=sinx` and `g(x)=x^2`
So,
`fog=f(g(x))=f(x^2)=sin (x^2)`
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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

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

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

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

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  7. If f(x)=1/x and g(x)=0 are two real functions, show that fog is not...

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  8. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

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  9. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3)- fog(5/3)

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  10. Let f(x)=[x] and g(x)=|x| . Find (f+2g)(-1)

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  11. Let fa n dg be real functions defined by f(x)=x/(x+1)a n dg(x)=1/(x+3)...

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  12. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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  13. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

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  14. If f(x) = x/(sqrt(1+x^2) then fofof(x)

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  15. Let f be a real function defined by f(x)=sqrt(x-1) . Find (fofof)(x...

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  16. If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x...

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  17. Find fog and gof , if f(x)=e^x , g(x)=(log)e x

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  18. Find fog and gof , if f(x)=x^2 , g(x)=cosx

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  19. Find fog and gof , if f(x)=|x| , g(x)=sinx

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  20. Find fog and gof , if f(x)=x+1 , g(x)=e^x

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