Given f(x)=x^2-+6 and g(x)=9-x^2,find f+g, f-g, gf, and f/g

Question

(f+g)(x)=

(f-g)(x)=

fg(x)=

f/g(x)=

Answer 1

(f+g)(x) = f(x)+g(x) = (x²+6)+(9-x²) = x²+6+9-x² = 15

(f-g)(x) = f(x)-g(x) = (x²+6)-(9-x²) = x²+6-9+x² = 2x²-3

fg(x) = f(x)*g(x) = (x²+6)(9-x²) = 9x²-x⁴+54-6x² = -x⁴+3x²+54

(f/g)(x) = f(x)/g(x) = (x²+6)/(9-x²)