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The relation f is defined by f(x)={{:(,x...

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

Answer

Step by step text solution for The relation f is defined by f(x)={{:(,x^(2), 0 le x le 3),(,3x,3 le x le 10):} The relation g is defined by g(x)={{:(,x^(2),0 le x le 2),(,3x,2 le x le 10):} Show that f is a function and g is not a function. by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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2 le 3x -4 le 5

If f: [0,3] to [0,3] is defined by: f(x) = {{:(1+x,0 le x le 2),(3-x, 2 lt x le 3):} , then show that f[0,3] sube [0,3] and find fof.

Knowledge Check

  • If f: R to R defined by f(x) ={{:(2x+5, if, x gt 0),(3x-2, if, x le 0):} then f is

    A
    a function
    B
    one one
    C
    onto function only
    D
    one one onto

  • If f: A to A is defined by f(x) =x^(3) , where A ={x//-1 le x le 1} , then f is

    A
    only one-one
    B
    only onto
    C
    bijection
    D
    not a function

  • If f is defined by f (x) = {:{ (x , " for " 0 le x lt 1) , ( 2 -x , " for " x le 1 ) :} then at x =1

    A
    Continuous and differentiable
    B
    Continuous but not differentiable
    C
    Discontinuous but differentiable
    D
    Neither continuous nor differentiable

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