Question

The function varies inversely with x and when x = 16.
f(x)
f(x) = 2
What is when x = 4?
f(x)

Answer 1

when x = 4 then f(x) equals 8

Explanation:

The complete question is as follows:

___________________________________________

The function f(x) varies inversely with x and f(x)=2 when x=16.

What is f(x) when x=4?

128

72

40

8

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Inversely proportional means that if you held constant all other variables, then one variable decreases if the other variable increases. Hence $y$ varies inversely as $x$ or $y$ is inversely proportional to $x$ if and only if:

$y=\frac{k}{x} \\ \\ \ k \ is \ any \ non-zero \ constant \ and \ is \ called \ constant \ of \ proportionality$

In this case:

$y=f(x) \\ \\ So: \\ \\ x=16 \\ \\ y=f(16)=2 \\ \\ k=yx \\ \\ k=(2)(16) \\ \\ k=32$

So our expression is:

$y=\frac{32}{x}$

We are asked to find f(x) when x=4, so:

$y=f(4)=\frac{32}{4} \\ \\ \boxed{y=f(4)=8}$

In conclusion, when x = 4 then f(x) equals 8

Learn more:

Direct Proportion: https://brainly.com/question/1620014

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