Home
Class 11
MATHS
If f(x)=x and g(x)=|x|, then define the ...

If `f(x)=x and g(x)=|x|`, then define the following functions:
`(i) f+g " "(ii) f-g`
`(iii) f*g" "(iv) (f)/(g)`

Text Solution

Verified by Experts

The correct Answer is:
(i) (f + g) (x) = `{{:(2x"," , x ge 0) , (0 "," , x lt 0):}` `" "(ii) (f-g)(x)={{:(0",",x ge 0),(2x",",x lt 0):}`
`(iii) (f*g)(x)={{:(x^(2)",",x ge 0),(-x^(2)",",x lt 0):} " "(iv)((f)/(g))(x)={{:(0",",x ge 0),(-1",",x lt 0):}`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercise 2 F|10 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercise 2 G|10 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercise 2D|18 Videos

  • PROBABILITY

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|10 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|32 Videos

Similar Questions

Explore conceptually related problems

If f and g are functions defined by : f(x) =sqrt(x - 1), g(x) = (1)/(x) , then describe the following : (i) f + g (ii) f - g (iii) fg (iv) (f)/(g) .

If f(x)=x^(2) and g(x)=2x , then evaluate, (i) (f+g)(3)" "(ii) (f-g)(2) (iii) (f*g)(1)" "(iv) ((f)/(g))(5)

Knowledge Check

  • If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

    A
    4
    B
    `1/4`
    C
    2
    D
    `1/2`

  • If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

    A
    `2x`
    B
    `2.f(x)`
    C
    `[f(x)]^2`
    D
    none of these.

    • Similar Questions

    Explore conceptually related problems

    If f and g are two real valued functions defined as f(x) =2x +1 and g (x) =x^(2) +1 then find (i) f+g (ii) f-g (iii) fg (iv) (f)/(g)

    Let f(x) = x^2 and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f –g) (x), (fg) (x), (f/g ) (x)

    If the functions are defined as f(x)=sqrtx and g(x) = sqrt(1-x) , then what is the common domain of the following functions : f+g, f//g, g//f, f-g " where " (fpm g)(x)=f(x) pm g(x),(f//g)(x)=(f(x))/(g(x))

    If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: f-g

    Let f(x) = x^(2) and g(x) = 2x + 1 be two real functions. Find : (f + g) (x), (f - g) (x), (fg) (x) and ((f)/(g)) (x) .

    Let f and g be two functions defined by: f(x) = sqrt(x-1) and g(x) = sqrt(4-x^(2)) Find (i) f+g (ii) g + f (iii) f-g (iv) g-f (v) fg (vi) gf (vii) (f)/(g) (viii) (g)/(f)

    Home
    Profile