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

If `f(x)=1/(2x+1),\ x!=-1/2,\ ` then show that `f(f(x))=(2x+1)/(2x+3)` , provided that `x!=-3/2dot`

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Given` f(x)=frac{1}{2 x+1}`
Replace x by f(x), we get,
` f[f(x)]=frac{1}{2 f(x)+1}`
` therefore f[f(x)]=frac{1}{2(frac{1}{2 x+1})+1}`
` ...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. 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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  2. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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

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

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

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

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

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

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

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

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  11. Find fog and gof , if f(x)=sin^(-1)x , g(x)=x^2

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  12. Find fog and gof , if f(x)=x+1 , g(x)=sinx

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  13. Find fog and gof , if f(x)=x+1 , g(x)=2x+3

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  14. Find fog and gof , if f(x)=c ,\ c in R , g(x)=sinx^2

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  15. Find fog and gof , if f(x)=x^2+2 , g(x)=1-1/(1-x)

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  16. Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .

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  17. L e tf: R->R :f(x)=|x|, Prove that fof=f

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  18. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  19. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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  20. If f(x)=2x+5 and g(x)=x^2+1 be two real functions, then describe f^...

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