Home
Class 12
MATHS
If f(x) = x/(sqrt(1+x^2) then fofof(x)...

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

Text Solution

Verified by Experts

fof of `(x)=f of (frac{x}{sqrt{1+x^{2}}})`
` =f(frac{frac{x}{sqrt{1+x^{2}}}}{sqrt{1+frac{x^{2}}{1+x^{2}}}})`
` =f(frac{x}{sqrt{1+2 x^{2}}})`
` =(frac{x}{sqrt{1+2 x^{2}}}.`
` .=frac{x^{2}}{1+frac{x}{1+2 x^{2}}})`
` sqrt{1+3 x^{2}}`
`
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

If f:R to R be defined by f(x) = (x)/(sqrt(1 +x^(2) )), then (fofof)(x)= …………. .

If f(x) =(x-4)/(2sqrt(x)) , then f^(')(1) is equal to

f(x)=(1)/(sqrt(x^(2)-1))

f(x)=sqrt(x^(2)-x+1)

If f(x)=(x)/(sqrt(1-x^(2))),g(x)=(x)/(sqrt(1+x^(2))) then ( fog )(x)=

If f(x)=x(sqrt(x)-sqrt(x+1)) then f(x) is:

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |