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`

Options

A. `{0,-1,(-3+isqrt(3))/(2),(-3-isqrt(3))/(2)}`
B. `{0,1,-1}`
C. `{0, -1}`
D. empty

Answer

C

Explanation

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}.`