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Consider the function f(x) = {{:( x^(2) ...

Consider the function f(x) = `{{:( x^(2) - 1"," , -1 le x le 1) , ( lnx "," , 1 lt x le e):}`
Let `f_(1) (x) = f (|x|)`
`f_(2) (x) = |f(|x|)|`
`f_(3) (x) = f (-x)`
Now answer the question
If `f_(4) (x) = log_(27) (f_(3) (x) + 2) ` , then range of `f_(4) (x)` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Consider the function f(x) = {{:( x^(2) - 1"," , -1 le x le 1) , ( lnx "," , 1 lt x le e):} Let f_(1) (x) = f (|x|) f_(2) (x) = |f(|x|)| f_(3) (x) = f (-x) Now answer the question Number of integral solution of the equation f_(1) (x) = f_(2) (x) is (are )

    A
    4
    B
    3
    C
    2
    D
    1

  • Consider the function f(x) = {{:( x^(2) - 1"," , -1 le x le 1) , ( lnx "," , 1 lt x le e):} Let f_(1) (x) = f (|x|) f_(2) (x) = |f(|x|)| f_(3) (x) = f (-x) Now answer the question Number of positive solution of the equation 2f_(2) (x) - 1 = 0 is (are)

    A
    `{{:( 4 + x , : , x ge 0 ), ( 4 - x , : , x lt 0):}`
    B
    `{{:( 2 + x , : , x ge 0 ), ( 2 - x , : , x lt 0):}`
    C
    `{{:( 4 + x , : , x lt 0 ), ( 4 - x , : , x ge 0):}`
    D
    `{{:( 4 - x , : , x ge 0 ), ( x , : , x lt 0):}`

  • If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

    A
    `f(x)` is increasing on ` [ - 1, 2]`
    B
    `f(x)` is continuous on ` [ -1, 3]`
    C
    `f' (2)` does not exist
    D
    `f(x)` has the maximum value at ` x =2`

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