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

Let `f(x) = (x+1)^(2) - 1, (x ge - 1)`. Then, the set `S = {x : f(x) = f^(-1)(x)}` is

A

`{0, -1, (-3+isqrt(3))/(2),(-3-isqrt(3))/(2)},i=sqrt(-1)`

B

{0, 1, -1}

C

{0, -1}

D

empty

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) = (x+1)^(2)-1" "[because xge1]`
`=x^(2)+1+2x-1=x^(2)+2x`
`S={x : f(x)-=f^(-1)(x)}`
S is the set of point of intersection of (y = x) and tf.
Now, solve y = x and `f(x) = x^(2) + 2x`
`x^(2) + 2x = x`
`x^(2) + x = 0`
x(x+1)=0
x = 0 or x = - 1
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