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Let f(x) =(x+1)^(2) - 1, x ge -1 , IF f...

Let `f(x) =(x+1)^(2) - 1, x ge -1` , IF ` f(x):[-1,oo] -> [-1,oo]`
Statement 1: The set `{x : f(x) =f^(-1)(x)}= {0,-1}`
Statement-2: f is a bijection.

A

Statement 1 is ture, statement 2 is true, statement 2 is a correct explanation for statement 1.

B

Statement 1 is ture, statement 2 is true, statement 2 is not a correct explanation for statement 1.

C

Statement 1 is ture, statement 2 is false.

D

Statement 1 is false, statement 2 is true.

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Let f:[-1,oo] in [-1,oo] be a function given f(x)=(x+1)^(2)-1, x ge -1 Statement-1: The set [x:f(x)=f^(-1)(x)]={0,1} Statement-2: f is a bijection.

Let f (x) = (x +1)^(2) -1 ( x ge -1). Then the number of elements in the set S = {x :f (x) = f ^(-1)(x)} is

Knowledge Check

  • If f(x) = (x+1)^2 – 1, x ge – 1 . Then, Statement I The set {x:f(x) = f^(-1) (x)} = {0, - 1). II f is a bijection .

    A
    Statement I is correct, Statement II is correct, Statement II is I correct explanation for statement I
    B
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    C
    Statement I is correct, II is incorrect
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  • Let f be a function defined by f(x)=(x-1)^(2)+x, (x ge 1) . Statement-1: The set [x:f(x)=f^(-1)(x)]={1,2} Statement-2: f is a bijectioon and f^(-1)(x)=1+sqrt(x-1), x ge 1

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  • Let f be a function defined by f(x)=(x-1)^(2)+1,(xge1) . Statement 1: The set (x:f(x)=f^(-1)(x)}={1,2} Statement 2: f is a bijection and f^(-1)(x)=1+sqrt(x-1),xge1 .

    A
    Statement -1 is true, Statement -2 is true and Statement -2 is correct explanation for Statement -1
    B
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