Physics, 24.04.2021 20:30 svalencia2

A girl kicks a soccer ball with a velocity of 20.0 m/s at 50.0°. What is the maximum height reached by the ball?

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we have been given a quadratic function $f(x)=(x-5)^{2} +2$ 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 $[2,\infty)$ .

if we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

let us know find its inverse.

$y=(x-5)^{2}+2$

upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

let us now solve this function for y.

$(y-5)^{2}=x-2\\ y-5=\pm \sqrt{x-2}\\ y=5\pm \sqrt{x-2}\\$

hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

Answer from: Quest

If one were to put the y value into the equation, they could find out what x is for a certain value of y. putting in the value of y (1), we get the equation: 1=4x-12=4xx=0.5this means that the value of x when why is 1 is x=0.5

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A girl kicks a soccer ball with a velocity of 20.0 m/s at 50.0°. What is the maximum height reached...

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