Question

Verify that the functions f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. Please show all of your work.
(see attached equation)
Verify that the functions f and g, are inverses of each other by showing that f(g(x))=x and g(f(x))=x. Please show all of your work.
(see attached equation)
@Mathematics

Answer 1

\[f(g(x))=\frac{2}{g(x)+6}=\frac{2}{\frac{2}{x}-6+6}\]
\[f(g(x))=\frac{2}{\frac{2}{x}}=x\]
\[g(f(x))=\frac{2}{f(x)}-6=\frac{2}{\frac{2}{x+6}}-6\]
\[g(f(x))=x+6-6=x\]

Answer 2

Thank you!