Home
Class 11
MATHS
The relation f is defined by f(x)={x^2,0...

The relation f is defined by `f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10`The relating g is defined by `g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10`Show that f is a function and g is not a function.

Text Solution

Verified by Experts

The correct Answer is:
N/a

At x = 3
`f(3)=3^(2)=9`
and `f(3)=3xx3=9`
`because` f has a unique value at x = 3
Therefore, f is a function. But , at x=2
`g(2)=2^(2)=4`
and `g(2)=3xx2=6`
`because` g has no unique value at x = 2.
`therefore` g is not a function.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2.3|5 Videos
  • PROBABILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|10 Videos
  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|32 Videos

Similar Questions

Explore conceptually related problems

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relation g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", "2 le x le 5):}. The relation g is defined by g(x) ={(3x+2", "0le x le1),(x^(3)", "1 le x le 5):} Show that f is a function and g is not a function

Redefine the function f(x)=|x-2|+|2+x|,-3lt=xlt=3

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

if f(x)={x^3+x^2,for0lt=xlt=2x+2,for2

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

The function f is defined by f(x)={{:(x+3" if ",xlt1),(x^(2)" if ",xge1):} . Find f(-5),f(1), and f(3) .

Discuss the continuity of the function f, where f is defined by f(x)={{:(3, if0lt=xlt=1),( 4, if1 < x < 3),( 5, if3lt=xlt=10):}

Verify Rolles theorem for the function f(x)=x(x-3)^2,\ 0lt=xlt=3 .

Let f(x)={x/2-1,0lt=xlt=1 1/2,1lt=xlt=2}g(x)=(2x+1)(x-k)+3,0<=x<=oo then g(f(x)) is continuous at x=1 if k equal to: