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

Name: Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x 2 - 6, x$\ge$ 0
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Question

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

Quizplus · Accepted Answer

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

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 $f ( x ) = \sqrt { x + 6 }$