Home
Class 11
MATHS
Let f,g: R rarr R be defined, respectiv...

Let f,g: R `rarr` R be defined, respectively by `f (x) = x + 1,g (x) = 2x -3`. find `f + g,f - g` and `f/g`

Text Solution

Verified by Experts

`(f+g) x=f(x)+g(x)=x+1+2 x-3=3 x-2`
`(f-g) x=x+1-(2 x-3)=4-x`
`(f/g) x=x+1/2 x-3, x ne 3/2`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|89 Videos
  • SEQUENCES AND SERIES

    V PUBLICATION|Exercise QUESTIONBANK|140 Videos

Similar Questions

Explore conceptually related problems

Let f, g: R rarr R be functions defined respectively by f(x)=x+1, g(x)=2 x-3 Find fg.

Function f :RrarrR are defined respectively,by f(x)=x^2+3x+1,g(x)=2x-3 ,find fog

Function f :RrarrR are defined respectively,by f(x)=x^2+3x+1,g(x)=2x-3 ,find gof

Let f, g: R rarr R be defined by f(x)=x^2+1 and g(x)=sin x . Find f o g and gof .

If f, g: R rarr R are defined by f(x)=x^2+3 x+1 , g(x)=2 x-3 , find (i) fog (ii)fof (iii) (gof) (2) (iv) (gog)(-5)

Let f: R rarr R be a function defined by f(x)=x^2-3 x+2 Find f^' (2) and f^'(6)

Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions defined by f(x)=x^2-x, x in A and g(x)=2|x-1/2|-1, x in A .Are f and g equal?. Justify your answer.

Consider the function f:R rarr R defined by f(x)=|x-1| .(iii)If g(x)=|x+1| ,find (f+g) and (f-g).

If f(x)=x^3+5x and g(x)=2x+1 ,find (f+g)(2) and (fg)(1) .

Find g o f and f o g , if f: R rarr R and g: R rarr R are given by f (x)=cos x and g(x)=3 x^2 . Show that gof ne f o g .

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTIONBANK
  1. Find the domain and range of the following functions. f(x)=abs[x-1]

    Text Solution

    |

  2. Let f={(x,x^2/(1+x^2)),x in R} be a real function from R to R. Deter...

    Text Solution

    |

  3. Let f,g: R rarr R be defined, respectively by f (x) = x + 1,g (x) = 2...

    Text Solution

    |

  4. Let f = {(1,1), (2,3),(0, -1), (- 1, - 3)} be a function from Z to Z d...

    Text Solution

    |

  5. Let R be a relation from N to N defined by R = {(a,b) in N and a = b^2...

    Text Solution

    |

  6. Let A = {1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5),(2,9),(3,1),(4...

    Text Solution

    |

  7. Let f be the subset of Z xx Z defined by f = {(ab, a + b) : a,b in Z} ...

    Text Solution

    |

  8. Let A = {9,10,11,12,13} and let f : A rarr N be defined by f (n) = the...

    Text Solution

    |

  9. A relation R is defined on the set Z of integers as follows.R ={ (x, y...

    Text Solution

    |

  10. Let A={1 ,2,3,4,5} and B={1,2,3, ... ., 6,7} . If R be a relation from...

    Text Solution

    |

  11. Find the domain and range of the function f = {(x, (x^2 -1)/(x - 1)): ...

    Text Solution

    |

  12. Let R be the relation on the set Z of all integers defined by R={(x, y...

    Text Solution

    |

  13. Let f be defined by f(x)=x-4 and g be defined by g(x)=(x^2-16)/(x+4), ...

    Text Solution

    |

  14. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

    Text Solution

    |

  15. Find the domain and range of the following functions: i)f(x)=1/(sqrt(x...

    Text Solution

    |

  16. Let f and g be two real functions defined by f(x)=1/(x+4) and g(x)=(x+...

    Text Solution

    |

  17. Which of the following relations are functions? Give reasons. If it is...

    Text Solution

    |

  18. If f(x)=x^2+x-1 and g(x)=4 x-7. be real functions then find: i) (f+g)...

    Text Solution

    |

  19. Let f and g be real functions defined by f(x)=sqrt(x+4), x ge-4 and g(...

    Text Solution

    |

  20. If af(x)+bf (1/x)=1/x-5 for x ne 0, where a ne b. Find f(x)

    Text Solution

    |