Question

Q(x)= 2x+2 R(x)=x^2-1 find (r•q)(5) and (q•r)(5)

Answer 1

Q(x) = 4

R(x) = 0

Explanation:

Q(x) = 2x + 2 ----- (1)

R(x) = x² - 1 -------- (2)

i) For (R * Q)(5) and [(Q * R)], we have as follow:

[(x² - 1)(2x + 2)] (5)

= (2x³ + 2x² - 2x - 2)(5)

= x³ + x² - x - 1

When x = -1

x³ + x² - x - 1 = 0

∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1

If x + 1 = 0

x = -1

and x² - 1 = 0

x = 1

From (1), when x= 1: Q(x) = 4

From (2), when x= 1 or -1: R(x) = 0