Function Problem

Question

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

 

r(x)=2x³

s(x)=x²

 

Write the expressions for (r-s)(x) and (r·s)(x) and evaluate (r+s)(2)

Answer 1

Colin:

 

1) Write the expressions for (r-s)(x) and (r·s)(x) and evaluate (r+s)(2)

 

(r-s)(x) = r(x) - s(x) = 2x³ - x²,  (r.s)(x) = r(x).s(x) = 2x⁵, (r o s)(x) = r(s(x)) = 2[(x²)]³ = 2x⁶.

 

2) (r+s) (2) = r(2) + s(2) = 2(2)³ + 2² = 16 + 4 = 20.

 

Dr. G.