Question

Find the inverse of y=x2-10x

Answer 1

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

Answer 2

`y=5\pm √((25+x))`

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=(-b\pm √(b^2-4ac))/(2a)`

`y=(-(-10)\pm √((-10)^2-4(1)(-x)))/(2(1))`

`y=(10\pm √(100+4x))/(2)`

`y=(10\pm √(4*25+4x))/(2)`

`y=(10\pm √(4(25+x)))/(2)`

`y=(10\pm 2√((25+x)))/(2)`

`y=5\pm √((25+x))`

Therefore, the inverse function for our given function would be
`y=5\pm √((25+x))`.