8) Suppose fíx) - x + 1 and g(x) x-4. (objective 3-algebraic operations on funct

Question

8) Suppose fíx) - x + 1 and g(x) x-4. (objective 3-algebraic operations on functions) a) What is (f + g)(x)? Answer:_ b) What is (f - g)(x)? What is (f+ g)(2)? Answer What is (f-)(-1)? Answer What is (fg)(6)? Answer What is (f/g)(5)? Answer: Answer c) What is (fg)(x)? Answer: d) What is (f/g)(x)? Answer functions. (objective 3- algebraic operations on functions) a) f g Answer:_ b) g f Answer: c) g g Answer: 10) Let d(t) be the number of dogs in the United States in year t, and let c(t) be the number of cats in the United States in year t, where t = 10 corresponds to 2010, (extra credit-3 points) a) Find the function p(t) that represents the total number of dogs and cats in the United States. b) Interpret the value of p(13). c) Let n(t) represent the population of the United States in year t, where t 10 corresponds to 2010. Find and interpret n(t)- pt). (Hint: Just provide an algebraic expression for p(t) that involves a sum) n(t)

Explanation / Answer

8. f(x)= x2+1

g(x)= x-4

a. (f+g)(x)= f(x)+g(x)= x2+x-3

(f+g)(2)=22+2-3=4+2-3=3

b.(f-g)(x)=f(x)-g(x)= x2-x+5

(f-g)(-1)= (-1)2-(-1)+5= 1+1+5=7

c.(fg)(x)= (x2+1)(x-4)=x3-4x2+x-4

(fg)(6)= 63 -4(6)2+6-4=216-144+6-4=74

d.(f/g)(x)=f(x)/g(x)= (x2+1)/(x-4)

(f/g)(5)= (25+1)(5-4)=26

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