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Let $f (x) = {(x + 1)}^{2} - 1 (x \geq - 1) .$ Then the set
$S = {x : f (x) = f^{- 1} (x)}$ contains

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0,−1,−3+i32,−3−i32

{0,1,–1}

{0,–1}

none of these

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detailed solution

Correct option is C

f(x)=f−1(x)⇒f(f(x))=x⇒(x+1)2−1+12−1=x. ⇒(x+1)2=x+1⇒x=0 or x=−1So S={0,–1}.

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Let f(x)=(x +1)2 –1(x ≥–1). Then the set S={x:f(x)=f-1(x)} contains

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Ready to Test Your Skills?

free study material

Let $f (x) = {(x + 1)}^{2} - 1 (x \geq - 1) .$ Then the set
$S = {x : f (x) = f^{- 1} (x)}$ contains