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Ajinkya Prabhat Vohra
Asked: 2022-11-07T15:19:12+05:30 In:

Let `f(x)=(x+1)^2-1, xgeq-1.`Then the set `{x :f(x)=f^(-1)(x)}`is`{0,1,(-3+isqrt(3))/2,(-3-isqrt(3))/2}`(b) `{0,1,-1“{0,1,1}`(d) `e m p t y`
A. `{0,-1,(-3+isqrt(3))/(2),(-3-isqrt(3))/(2)}`
B. `{0,1,-1}`
C. `{0, -1}`
D. empty

Let `f(x)=(x+1)^2-1, xgeq-1.`Then the set `{x :f(x)=f^(-1)(x)}`is`{0,1,(-3+isqrt(3))/2,(-3-isqrt(3))/2}`(b) `{0,1,-1“{0,1,1}`(d) `e m p t y`
A. `{0,-1,(-3+isqrt(3))/(2),(-3-isqrt(3))/(2)}`
B. `{0,1,-1}`
C. `{0, -1}`
D. empty
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  1. Correct Answer – C
    Since `f(x) = (x+1)^(2)-1` is continuous function, solution of
    `f(x)=f^(-1)(x)` lies on the line `y=x`. Therefore,
    `f(x)=f^(-1)(x)=x`
    ` or (x+1)^(2)-1=x`
    ` or x^(2)+x=0`
    i.e., ` x=0 or -1`
    Therefore, the required set is `{0,-1}.`

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