Answer:
they are NOT inverses
Step-by-step explanation:
f(g(x)) = (√(x+3))² -3 = x +3 -3 = x . . . . f is the inverse of g on g's domain
g(f(x)) = √(x²-3 +3) = √(x²) = |x| . . . . . . g is not the inverse of f, except on a restricted domain (x > 0)
Since the relationship is one-sided, we have to say that the functions are NOT the inverses of each other.
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Consider the attached graph.
Functions are inverses of each other if one is a reflection of the other in the line y=x (the dashed orange line). Here, only the "beaded" portion of f(x) (red) matches the reflection of g(x) (blue). The "inverses of each other" relationship is not complete.
