# How do you find #f(20)#, if #f(x)# varies inversely with #x# and #f(12)=5#?

To find f(20) when f(x) varies inversely with x and f(12) = 5, we can use the inverse variation formula.

The inverse variation formula states that if y varies inversely with x, then the product of x and y remains constant. Mathematically, this can be represented as xy = k, where k is the constant of variation.

In this case, we are given that f(x) varies inversely with x. So, we can write the equation as f(x) * x = k.

To find the value of k, we can use the given information that f(12) = 5. Plugging these values into the equation, we get 5 * 12 = k, which gives us k = 60.

Now that we have the value of k, we can find f(20) by plugging it into the equation. f(20) * 20 = 60. Solving for f(20), we get f(20) = 60/20 = 3.

Therefore, f(20) is equal to 3.

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If (f(x)) varies inversely with (x), it means that (f(x) \cdot x = k), where (k) is a constant. We can find the value of (k) using the given information, (f(12) = 5).

[f(12) \cdot 12 = k] [5 \cdot 12 = k] [k = 60]

Now, we can use this value of (k) to find (f(20)).

[f(20) \cdot 20 = 60] [f(20) = \frac{60}{20}] [f(20) = 3]

Therefore, (f(20) = 3).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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