The question:
Suppose you have a function given by $f(x)=0.1x^2-x+2.5$
We are given that
$f(x_1)=3$
$f(x_2)=1.5$
We are tasked with finding the distance between $x_1$ and $x_2$
My attempt so far:
I tried to find the solutions in each case using the quadratic formula, I was then going to subtract one x value from the x value found in the other solutions, but there are two problems come with doing that
There's two solutions for each value of $f(x)$ though by graphing we can figure out which would be reasonable
For the case where $f(x)=1.5$ we get imaginary solutions
My other thoughts :
I thought maybe something to do with finding the rate of change using differentiation and then noting that the distance between one of the $f$ values is half the other
But I don't that will work because it's a curve not a line and also I want to find a solution using more elementary methods . Like algebra.
Can anyone please help me out here?