R (x) = - x² + 3x s (x) = 2x + 1

(s - r) (x) =

(s-r) (x) = x²-x+1

Step-by-step explanation:

We have given two functions.

r (x) = - x²+3x and s (x) = 2x+1

We have to find the difference of two functions.

(s-r) (x) = ?

The formula to find the difference of two functions is:

(s-r) (x) = s (x) - r (x)

Putting the value of given functions in above formula, we have

(s-r) (x) = (2x+1) - (-x²+3x)

(s-r) (x) = 2x+1+x²-3x

(s-r) (x) = x² + (-3+2) x+1

(s-r) (x) = x² + (-1) x+1

(s-r) (x) = x²-x+1 which is the answer.

r (x) = - x² + 3x

s (x) = 2x + 1

(s - r) (x) is simply the difference of these functions. Subtract r (x) from s (x):

(s - r) (x) = s (x) - r (x)

(s - r) (x) = 2x + 1 - (-x² + 3x)

(s - r) (x) = 2x + 1 + x² - 3x

(s - r) (x) = x² - x + 1