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Aleks [24]
3 years ago
11

A boat goes 4 miles upstream in four hours. It returns downstream to the starting point in two hours .The rate of the boat is X.

The rate of the river current is Y . Find X &Y miles per hour
Mathematics
1 answer:
Anna71 [15]3 years ago
5 0
The boat(x) goes 1mi/hr because 4 mi and 4hr divide each by four. The rate of the river current S twice that because the time is halved so y=8mi/hr
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Write the inverse function for the function, ƒ(x) =1/2x + 4. Then, find the value of ƒ^ -1(4). Type your answers in the box.
Kipish [7]

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f⁻¹(x) = 2x - 8

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Step-by-step explanation:

f(x) = \frac{1}{2} x + 4\\x = \frac{1}{2} f^{-1}(x) + 4\\x - 4 = \frac{1}{2} f^{-1}(x)\\2x - 8 = f^{-1}(x)\\f^{-1}(x) = 2x - 8

Let's test it

f^{-1}(f(x)) = 2(f(x)) - 8\\f^{-1}(f(x)) = 2( \frac{1}{2}x + 4) - 8\\f^{-1}(f(x)) = \frac{2}{2}x + 8 - 8\\f^{-1}(f(x)) = x

So we do indeed have the inverse function, so using that we can plug in the values requested:

f⁻¹(x) = 2x - 8

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