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Question 298792: Are functions f(x) = -1/4x + 5/4 and g(x) = -4x + (2.5/.5) inverses of each other? Why?
Must be solve in algebraic based.
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! We can use the Round-Trip Theorem to show that if both functions = x, then they are inverses of each other.
In other words, if g(f(x)) = x and f(g(x)) = x, then the functions are inverses of each other.
g(f(x)) = -4[(-x/4) + 5/4] + 2.5/0.5
g(f(x)) = (x - 5) + 2.5/0.5
g(f(x)) = x - 5 + 5
g(f(x)) = x
Now, I will plug the value of g(x) into f(x). If I get x as the answer, then both functions are inverses of each other.
f(g(x)) = (-1/4)[(-4x) + (2.5/0.5)] + (5/4)
f(g(x)) = (x - (5/4) + (5/4)
f(g(x)) = x
As you can see they both = x and so they are both inverses of each other.
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