Home
Class 12
MATHS
If a function f is defined as f(x)={(|x-...

If a function `f` is defined as `f(x)={(|x-4|)/(x-4)\ \ \ ,\ \ \ x!=4 0\ \ \ ,\ \ \ x=4` Show that `f` is everywhere continuous except at `x=4` .

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is :

f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

Knowledge Check

  • If a function f:RtoR is defined by f(x)=(x^(2)-5)/(x^(2)+4) , then f is

    A
    one-one but not onto
    B
    onto but not one-one
    C
    neither one-one nor onto
    D
    a bijection

  • The function f is defined as f(x) = -4x^(3) - 4x^(2) . What is f(-4) ?

    A
    `-320`
    B
    `-192`
    C
    16
    D
    192

  • The range of the function f(x)=(|x-4|)/(x-4) is

    A
    A. `[1,oo)`
    B
    B. `{-1,1}`
    C
    C. `R`
    D
    D. `{-1,3}`

    • Similar Questions

    Explore conceptually related problems

    A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equals

    If f(x)={(x-4)/(|x-4|)+a ,\ \ \ if\ x 4 is continuous at x=4 , find a ,\ b .

    The function f(x) is defined by f(x)={log_[4x-3](x^2-2x+5) if 3/4 1 4 when x=1}

    If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

    If a function f:[2,oo)toR is defined by f(x)=x^(2)-4x+5 , then the range of f is

    Home
    Profile