Determine Algebraically Whether F and G Are Inverse Functions $f ( x ) = \sqrt { x + 6 }$

Multiple Choice

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x² - 6,x ? 0

A) Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = x + 6 - 6 = x$
B) No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$