Question 1000011: Hello, I don't understand one-to-one functions. They are supposed to be solved algebraically.
Q: Let f be a one-to-one function and suppose g is the inverse function of f. If f(8)=6 and f(1)=8, find g(8).
There isn't a equation for me to plug anything in so how would I solve it? Thanks for the help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q: Let f be a one-to-one function and suppose g is the inverse function of f. If f(8)=6 and f(1)=8, find g(8).
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Note: Every line that is not perpendicular to or parallel to the
x=axis is one-to-one.
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You have two points for "f": (8,6) and (1,8)
Therefore you have two points for the inverse of "f":: (6,8) and (8,1)
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slope of g :: (1-8)/(8-6) = -7/2
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Form::
y = mx + b
Solve for "b"::
1 = (-7/2)8 + b
b = 1 + 28
b = 29
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Ans: g(x) = (-7/2)x + 29
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Cheers,
Stan H.
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