Suppose that the functions r and s are defined for all real numbers x as follows.

Question

r(x)=x+5

s(x)=2x^2

Write the expressions for (r+s)(x) and (r·s)(x) and evaluate (r-s)(3).

Answer 1

(r+s)(x) = x+5+2x² (No like terms to combine, so this is the final answer) Written with decreasing exponents order: 2x²+x+5

(r·s)(x) = (x+5)(2x²) Using the distributive property, (2x²)(x)+ (2x²)(5) = 2x³ +10x²

Next, plug in 3 into the subtraction expression to evaluate.

(r-s)(3) = 3+5-2(3)² Follow the order of operations

= 3+5-2(9)

= 3+5-18

= 8-18 = -10

Answer 2

For

r(x) = x + 5

s(x) = 2x²

(r + s)(x) = r(x) + s(x) = x + 5 + 2x²

I'm assuming (r•s) = (r*s) below

(r*s)(x) = r(x)*s(x) = (x + 5)(2x²) = 2x³ + 10x²

And

(r - s)(x) = r(x) - s(x) = x + 5 - 2x²

(r - s)(3) = 3 + 5 - 2(3²)

(r - s)(3) = 3 + 5 - 2(9)

(r - s)(3) = 3 + 5 - 18

(r - s)(3) = -10

I hope you find this useful send a message if you have any questions.