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The number of continuous functions on R which satisfy \mathrm{(f(x))^2=x^2} for \mathrm{x \in R} is
 

Option: 1

2


Option: 2

4


Option: 3

1


Option: 4

 infinitely many


Answers (1)

best_answer

\begin{aligned} & \mathrm{ f(x)=x, f(x)=-x, f(x)=}\left\{\begin{aligned} \mathrm{x,} & \mathrm{x \geq 0} \\ \mathrm{-x,} &\mathrm{ x<0 }\end{aligned}\right. \\ &\mathrm{ f(x)=}\left\{\begin{aligned} \mathrm{-x,} &\mathrm{ x \geq 0 }\\ \mathrm{x, }&\mathrm{ x<0 }\end{aligned}\right. \end{aligned}

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