Question

Let f(x) = x^2 – 3x + 8 and
g(x) = x – 5

(a) Find the sum (f + g)(x) and simplify the results.

(b) Find the composite function
(f º g)(x) and simplify the results.


(c) Find (f º g)(2)
Show some work.


(d) Find the composite function of (g º f)(x) and simplify the results.

Answer 1

f(x) = x^2 – 3x + 8
g(x) = x – 5

a) (f+g)(x) = x^2 - 3x + 8 + x - 5

= x^2 -2x + 3

testing:
let x=5
f(5) = 25 - 15 + 8 = 18
g(5) = 0

so f(5) + g(5) = 18+0 = 18
(f+g)(5) = 25 - 10 + 3 = 18


b)
(f º g)(x)
= f(g(x))
= f(x-5)
= (x-5)^2 - 3(x-5) + 8
= x^2 - 13x + 48

c) then (f º g)(2)
= 4 - 26 + 48
= 26

or
f(g(2))
= f(-3)
= 9 + 9 + 8
= 26

d) (g º f)(x)
= g(f(x))
= g(x^2-3x+8)
= x^2-3x+8 - 5
= x^2 - 3x + 3

Answer 2

Wow this is confusing. Can you explain how you got each answer please? Thank you!