Algebra
posted by Carmin .
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.

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 
Wow this is confusing. Can you explain how you got each answer please? Thank you!
Respond to this Question
Similar Questions

Intermediate Algebra
I have a take home test and I'm stuck on a couple. Anyone help please? 
Algebra
When Let f (x) = x^2 – 3x + 8 and g(x) = x – 5 Find Find the composite function of (fºg)(x) and simplify Find (fºg)(2) Find the composite function (gºf)(x) 
Algebra
Let f (x) = x^2 – 3x + 8 and g(x) = x – 5. Find the sum (f + g) (x) and simplify the results. 
Algebra
Use the quadratic formula to find the exact solutions of the equation. Show work. Simplify the final results as much as possible. 4x^2 – 16x + 25 = 0. 
pre calculus
evaluate if possible the function at the given values(s) of the independent variable. Simplify the results. f(x)=7x4 a) f(0) b) f(3) c) f(b) d) f(x1) 
Algebra
1. Subtract and simplify 18/y8  18/8y 2. subtract simplify if possible v5/v  7v31/11v 3. Simplify by removing factors of 1 r^281/(r+9)^2 4. Divide and simplify v^216/25v+100 divided by v4/20 5. find all rational numbers for … 
Math
Let f(x)= 2x^2, g(x)= 5x6, and m(x)= 3x. Find and simplify the composite function g(m(f(x))). 
PreCal
For given functions f and g find formulas for a)f o g and b)g o f. Simplify results as much as possible. f(t)= t3/t+6 , g(t)= 1/(x+6)^2 
algebra
Let f(x)= 2x^2 +7 and g(x)= x – 6. (a) Find the composite function (f*g)(x) and simplify. Show work. (b) Find ( f*g)(1). Show work. 
precalc
Letf(x)=2x2 –5 and g(x)=x+4. (a) Find the composite function ( f o g)(x) and simplify. Show work. (b)Find (f og)(3).Showwork.