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Question Number 206764 by mustafazaheen last updated on 24/Apr/24

Answered by A5T last updated on 24/Apr/24

$$f\left(g(-3)\right)=f\left(\sqrt{-3}\right)=f\left(\sqrt{3}i\right)={\left(\sqrt{3}i\right)}^2=-3$$

Commented by JDamian last updated on 24/Apr/24

$$\sqrt{-3}\ne 3i$$$$\sqrt{-3}=\sqrt{3}i\Rightarrow {\left(\sqrt{3}i\right)}^2=-3$$$$$$$$becauseg\left(x\right)=f^{-1}\left(x\right)\Rightarrow f\circ g=g\circ f=x$$

Commented by mr W last updated on 24/Apr/24

$$forx\in R$$$$f_1\left(x\right)={\left(\sqrt{x}\right)}^{2}isvalidforx⩾0$$$$f_2\left(x\right)=x$$$$f_1(-3)\ne -3,because{f}_1(-3)isnotdefined.$$$$f_2(-3)=-3$$

Commented by A5T last updated on 24/Apr/24

$$Yea,itdependsonthedomain.$$

Answered by A5T last updated on 24/Apr/24

$$f\left(g\left(x\right)\right)={\left(\sqrt{x}\right)}^2=x\Rightarrow f\left(g(-3)\right)=-3$$

Answered by aba last updated on 29/Apr/24

$$-3$$

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