You and a friend have some pvc pipes of various lengths and a hacksaw. You select a 2.0 m long section of pipe that is open at both ends but your friend chooses a 0.60 m long section of pipe that is closed at one end. You want to cut your open pipe to a length that makes its no = 2 harmonic the same frequency as the closed-at-one-end pipe’s nc = 3 harmonic. How long should you make your pipe?

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

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