Show the algebraic justification that f and g are inverse functions
f(x) = 'squareroot' x-4 , x (greaterthan or equal to) 4
g(x) = x^2+4, x (greaterthan or equal to) 0
+23251 f(x) and g(x) will be inverse functions when f( g(x) ) = x and g( f(x) ) = x.
f(x) = sqrt( x - 4 ) [with x >= 4]
g(x) = x2 + 4 [with x >= o]
f( g(x) ) = f( x2 + 4 ) = sqrt( (x2 + 4) - 4 ) = sqrt( x2 + 4 - 4 ) = sqrt( x2 ) ) = x [Since x >= 0]
g( f(x) ) = g( sqrt( x - 4 ) ) = sqrt( x - 4 )2 + 4 = (x - 4) + 4 = x - 4 + 4 = x
Since f( g(x) ) = g( f(x) ) = 0, f(x) and g(x) are inverse functions.
