Posted by Carmin on .
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.

Algebra 
Reiny,
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(x5)
= (x5)^2  3(x5) + 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^23x+8)
= x^23x+8  5
= x^2  3x + 3 
Algebra 
Carmin,
Wow this is confusing. Can you explain how you got each answer please? Thank you!