Given that f(x) =(x-2)^2 and g(x)=6-5x 1. (f+g)(x)= 2. (f-g)(x)= 3. (fg)(x)= 4. (f/g)(x)=

Answer 1

Hi Giselle S.

You can look up the rules for Combination Functions in your text or online. The Combinations are Sum, Difference, Product and Quotient please see below where I worked through the first two.

For your questions you just need to follow the given operations, combine like terms

f(x) = (x-2)² and g(x) = 6 - 5x, then (f + g)(x) = f(x) + g(x)

(f + g)(x) = just add the two functions as given

1) (f + g)(x) = (x - 2)² + (6 - 5x) = (x² - 4x + 4) + (6 - 5x) = x² - 4x + 4 + 6 - 5x = x² - 9x + 10

2) (f - g)(x) = (x - 2)² - (6 - 5x) = (x² - 4x + 4) - (6 - 5x) = (x² - 4x + 4) - 6 + 5x = x² - 4x + 4 - 6 + 5x = x² + x - 2 = (x + 2)(x - 1)

Can you work through the rest?

(f*g)(x) = (x - 2)² * (6 - 5x)

(f/g)(x) = (x - 2)²/(6 - 5x)

I hope this helps and do check the rules they are easy to follow. If you have any questions please write back.