If the function \( g \) is the inverse of the function \( f \), predict \( f(g(x)) \) and \( g(f(x)) \).
Answer (3)
If the function g is the inverse of the function f, then f(g(x)) = x and g(f(x)) = x. ;
f( g(x )) = x and g( f( x)) = x, for all values of x in their respective domains, because g is the inverse of the function f.
When g is the inverse of f , applying f to g ( x ) returns x and vice versa, expressed as f ( g ( x )) = x and g ( f ( x )) = x . This holds true for any pair of inverse functions. An example demonstrates these properties clearly with specific functions and simplifications.
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