Home
Class 12
MATHS
Let f,\ g and h be functions from R to R...

Let `f,\ g` and `h` be functions from `R` to `R` . Show that `(f+g)oh=foh+goh`

Text Solution

Verified by Experts

To show:
`(f+g)oh=foh+goh`
Let
`((f+g)oh)(x)`
`=(f+g)(h(x))`
`=f(h(x))+g(h(x))`
`=(foh)(x)+(goh)(x)`
`=(foh)+(goh)(x)`
...
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

Let f,\ g and h be functions from R to R . Show that (fg)oh=(foh)(goh)

Let f and g be two functions from R into R defined by f(x) =|x|+x and g(x) = x " for all " x in R . Find f o g and g o f

If f,g,\ h are three functions defined from R\ to\ R as follows: the range of h(x)=x^2+1

If f,g,\ h are three functions defined from R\ to\ R as follows: Find the range of f(x)=x^2

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

Let f and g be differentiable function of R such that g(x)<=0,AA x in R and consider h(x)={f(x)f or |f(x)|<=g(x) and g(x)f or f(x)

Let f : R to R : f (x) =10x +7. Find the function g : R to R : g o f = f o g =I_(g)

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

    Text Solution

    |

  2. If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such t...

    Text Solution

    |

  3. Let f,\ g and h be functions from R to R . Show that (f+g)oh=foh+goh

    Text Solution

    |

  4. Let f,\ g and h be functions from R to R . Show that (fg)oh=(foh)(goh)

    Text Solution

    |

  5. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

    Text Solution

    |

  6. Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx Q...

    Text Solution

    |

  7. Let f: RvecR and g: vecR be two functions such that fog(x)=sinx^2a n...

    Text Solution

    |

  8. If f: R->R be given by f(x)=sin^2x+sin^2(x+pi//3)+cosx\ cos(x+pi//3) f...

    Text Solution

    |

  9. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

    Text Solution

    |

  10. Let f: RvecR be a function given by f(x)=a x+b for all x in R . Find ...

    Text Solution

    |

  11. Let f: A->A be a function such that fof=f . Show that f is onto if and...

    Text Solution

    |

  12. Let f,g: RvecR be two functions defined as f(x)=|x|+x and g(x)=|x|-x ,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |