Algebra

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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 -

    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 -

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

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