Question

Find the difference of functions s and r shown

below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =

Answer 1

`\displaystyle (s-r)(x) = x^2 - x + 1`

Explanation:

We are given the two functions:

`\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1`

And we want to find:

`\displaystyle (s-r)(x)`

This is equivalent to:

`\displaystyle (s-r)(x) = s(x) - r(x)`

Substitute and simplify:

`\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}`

In conclusion:

`\displaystyle (s-r)(x) = x^2 - x + 1`