Given f(x)=(x=2)/3, and g(x)=2x^2-4 find a formula for the following:a. (f+ g)(x) b. (f/g)(x) c. (f◦g)(x) d. (g◦f)(x)

f(x)=(x-2)/3 and g(x) =2x^2-4

To find:

a. (f+ g)(x) = f(x)+g(x) = (x-2)/3 + 2x^2-4 = (6x^2+x-14)/3

b. (f/g)(x) = f(x)/g(x) = [(x-2)/3]/[2x^2-4 ] = (x-2)/{6(x^2-2)}

c. (f*g)(x) = f(x)*g(x) = (x-2)(2x^2-4)/3

d. (f-g)(x)  = f(x) -g(x) = (x-2)/3 -(2x^2-4) =(x-2-6x^2+12)/3 = (10+x-6x^2)/3