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Let f(x)={{:(1+x",", 0 le x le 2),(3-x",...

Let `f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):}`
find (fof) (x).

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The correct Answer is:
`A toR; Bto R; C to R; D to S`
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Knowledge Check

  • If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) is not differentiable at:

    A
    `x=1`
    B
    `x=2`
    C
    `x=5/2`
    D
    `x=3`

  • Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4], then

    A
    `a=1, b gt 5`
    B
    `a=2, b gt 7`
    C
    `a=2, b gt 10`
    D
    `a=0, b in R`

  • Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

    A
    continuous at x =1
    B
    Right continuous at x =1
    C
    Left continuous at x =1
    D
    Limit exists at x =1

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