Question

Find the inverse of y=x2-10x

Answer 1

Answer:

$y=5\pm \sqrt{(25+x)}$

Step-by-step explanation:

We are asked to find the inverse for the function $y=x^2-10x$.

We know that to find inverse, we interchange x and y values and then solve for y.

After interchanging x and y values, we will get:

$x=y^2-10y$

Switch sides:

$y^2-10y=x$

$y^2-10y-x=x-x$

$y^2-10y-x=0$

Now, we will use quadratic formula to solve for y.

$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}$

$y=\frac{10\pm \sqrt{100+4x}}{2}$

$y=\frac{10\pm \sqrt{4*25+4x}}{2}$

$y=\frac{10\pm \sqrt{4(25+x)}}{2}$

$y=\frac{10\pm 2\sqrt{(25+x)}}{2}$

$y=5\pm \sqrt{(25+x)}$

Therefore, the inverse function for our given function would be $y=5\pm \sqrt{(25+x)}$.

Answer 2

this is pretty hard but here is your answer 

y = x^2 - 10x + 25 - 25

 y = (x-5)^2 - 25

 y+25 = (x-5)^2

 x-5 = +/-sqrt(y+25)

 

 And you get TWO inverses:

 

 x = 5 + sqrt(y+25), for x>=5

 x = 5 - sqrt(y+25), for x<=5