Please help me... I really need help with the question above. Only real answers please
1 answer:
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.
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SOLUTION
From the question given the following statements to prove are correct, then the last part
The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem