Question

Let f(x) and g(x) defined as f(x) = x-5, g(x) = x²-1. Find:

a. f+g
b. f-g
c. f•g
d. f/g
e. g/f​

Answer 1

Step-by-step explanation:

(f+g)(x)=f(x)+g(x)

=x2+2x+1

(f−g)(x)=f(x)−g(x)

=x2−(2x+1)

=x2−2x−1

(fg)(x)=f(x).g(x)

=x2(2x+1)

=2x3+x2

(gf)(x)=g(x)f(x)          (g(x)=0)

=2x+1x2                         (x=−21)

Answer 2

Answer:

a. f+g = x-5 + x^2 -1

= x^2 + x - 6

b. f-g = x-5 - ( x^2 -1 )

= x-5 - x^2 + 1

= - x^2 + x -4

c. fog = f [g (x) ]

= f [ x^2 -1 ]

= x^2 -1 -5

= x^2 -6

d. f/g = x-5 /x^2 -1

e. g/f = x^2 -1 / x -5.