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inverse of y = x2 – 10x.?????????

I am having difficulty understanding how to find the inverse of the function ( y = x^2 - 10x ). Could someone please explain the steps involved in determining its inverse? Thank you!

2 Answers

A
Anonymous

Feb 04, 2025

This isn’t easy. First, there are multiple values of x for the same value of y, so there isn’t a proper inverse function on the whole domain. Here’s how you do it:

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

Hope this helped!

R
Reggie Barton

Jan 19, 2025

I’m no expert but I’m pretty sure it’s just over 1.

so

y = x2 – 10x

y[inverse] = (1) / (x2 – 10x)

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