Which type of function is it? (I)

Algebra Level 3

Let f : [ − 1 , 1 ] → [ − 1 , 1 ] f : [-1, 1] \to [-1, 1] be a function satisfying, for all x ∈ [ − 1 , 1 ] x \in [-1, 1] ,

f ( x ) = x × ∣ x ∣ f(x) = x \times {|x|}

Which of the following best describes f f ?

Neither Injective nor Surjective Injective but not Surjective Surjective but not Injective Bijective

Zeeshan Ali by Zeeshan Ali , 25, Pakistan

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1 solution

展豪 張
Mar 20, 2016

f ( x ) = { − x 2 , x < 0 x 2 , x ≥ 0 f(x)=\left\{ \begin{matrix}-x^2,x<0\\x^2,x\ge0\end{matrix}\right.
f ( x ) f(x) is increasing and continuous and f ( − 1 ) = − 1 f(-1)=-1 , f ( 1 ) = 1 f(1)=1 .
Therefore it is bijective.

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