Posted by **Carmin** on Wednesday, June 17, 2009 at 9:19am.

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**, Wednesday, June 17, 2009 at 9:55am
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

- Algebra -
**Carmin**, Wednesday, June 17, 2009 at 10:35am
Wow this is confusing. Can you explain how you got each answer please? Thank you!

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