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. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$

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To determine if two functions are inverses, we check if $f(g(x)) = x$ and $g(f(x)) = x$. The calculations for both $f(g(x))$ and $g(f(x))$ simplify to $x$, confirming that $f$ and $g$ are indeed inverse functions.

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

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