I NEED HELP PLEASE, THANKS! :) If a musical instrument such as a trumpet or flute is “flat”, should the pipe be lengthened or shortened?

Shortened

Explanation:

A longer pipe will have a longer wavelength, and therefore a lower frequency.

A shorter pipe will have a shorter wavelength, and therefore a higher frequency.

A "flat" note has a low frequency, so the pipe should be shortened.

The same phenomenon can be demonstrated with guitar strings.  The longer the string, the lower the pitch.

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 .