c-g 3.5.29 Use functions fx)-x2 -64 and g(x)--x+64 to answer the questions below

Question

c-g

3.5.29 Use functions fx)-x2 -64 and g(x)--x+64 to answer the questions below (a) Solve fix) = 0. (b) Solve g(x) #0. (c) Solve f(x) = g(x) (d) Solve f(x)>0 (e) Solve g(x) s 0 (0) Solve f(x)-g(x) (g) Solve f(ox)21 (a) The solution set is t -8,8 (Type an integer or a fraction. Use a comma to separate answers as needed.) (b) The solution set is {-88 } (Type an integer or a fraction. Use a comma to separate answers as needed.) (c) The solution set is (Type an integer or a fraction. Use a comma to separate answers as needed)

Explanation / Answer

a. f(x)=0

x2-64=0

x=-8,8

b.g(x)=0

-x2+64=0

x=-8,8

c.f(x)=g(x)

x2-64=-x2+64

2x2=128

x=-8,8

d.f(x)>0

x2-64>0

(x-8)(x+8)>0

(-infinity,-8)U(8,infinity)

e.g(x)<=0

-x2+64<=0

(8-x)(8+x)<=0

x>=8

(-infinity,-8]U[8,infinity)

f.f(x)>g(x)

x2-64>-x2+64

2x2-128>0

x^2-64>0

(-infinity,-8)U(8,infinity)

g. f(x)>=1

x2-64>=1

x2-65>=0

(-infinity,-sqrt65]U[sqrt65,infinity)

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