First slide

Functions (XII)

Question

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

Moderate

A

$\{0, - 1, \frac{- 3 + i \sqrt{3}}{2}, \frac{- 3 - i \sqrt{3}}{2}\}$
B

${0, 1, - 1}$
C

${0, - 1}$
D

$e m p t y$

Solution

$\sin c e f (x) = {(x + 1)}^{2} - 1 i s c o n t i n u o u s f u n c t i o n, s o l u t i o n o f f (x) = f^{- 1} (x) l i e s o n t h e l i n e y = x . T h e r e f o r e f (x) = f^{- 1} (x) = x$
${(x + 1)}^{2} - 1 = x \Rightarrow x^{2} + x = 0 \Rightarrow x = 0 o r - 1 T h e r e f o r e, t h e r e q u i r e d s e t i s \{0, - 1\}$

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