If $f ( x ) = \sqrt { 2 - 2 x }$ and $g ( x ) = \sqrt { x ^ { 2 } - 1 }$ , find $f + g$ , $\mathrm { fg }$ , and their domains.

Name: If $f ( x ) = \sqrt { 2 - 2 x }$ and $g ( x ) = \sqrt { x ^ { 2 } - 1 }$ , find $f + g$ , $\mathrm { fg }$ , and their domains.
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The Answer of If $f ( x ) = \sqrt { 2 - 2 x }$ and $g ( x ) = \sqrt { x ^ { 2 } - 1 }$ , find $f + g$ , $\mathrm { fg }$ , and their domains.

If f(x)=2−2xf ( x ) = \sqrt { 2 - 2 x }f(x)=2−2x​

If $f ( x ) = \sqrt { 2 - 2 x }$