Question

Choose the inverse of y = x2 – 10x.

Answer 1

`y=\pm√(x+25)+5`

Explanation:

Given function:

`y=x^2-10x`

Rearrange to make
`x` the subject.

First, complete the square by adding 25 to both sides and factoring:

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

`y+25=(x-5)^2`

Square root both sides:

`\pm√(y+25)=x-5`

Add 5 to both sides:

`x=\pm√(y+25)+5`

Finally, swap
`x` and
`y` (since the inverse of a function is its reflection in the line
`y = x`)

`y=\pm√(x+25)+5`

Answer 2

The inverse is 5±sqrt(x+25)

Explanation:

y = x^2 - 10x

To find the inverse, exchange x and y and solve for y

x = y^2 -10y

Complete the square

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

x+25 = (y-5)^2

Take the square root of each side

±sqrt(x+25) = y-5

Add 5 to each side

5±sqrt(x+25) = y

The inverse is 5±sqrt(x+25)